Method for determining errors in a rotation position determination system

ABSTRACT

A method for determining one or more errors of a rotational position establishment system is provided. More particularly, a rotary apparatus having first and second parts that rotate relative to one another about a rotation axis of the rotary apparatus is used to determine one or more rotation errors. A rotation position determination system is used to determine rotation position errors from the rotation positions of the rotary apparatus or a change in the rotation position of the rotary apparatus, and from rotation positions of a reference rotary apparatus or a change in the rotation position of the reference rotary apparatus.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a method for establishing errors of arotational position establishment system and an arrangement forperforming such a method.

Rotational devices, such as rotary pivot joints or rotary tables,generally comprise a rotational position establishment system, inparticular an angle encoder, so as to be able to register the currentrotational angle of part of the device about a rotational axis. In thecase of conventional incremental measuring systems, this is usuallybrought about with reference to a reference marker. However, theconventional angle measuring systems have errors which lead tomeasurement errors in coordinate metrology. The positioning accuracy inthe case of the rotation about the rotational axis is therefore linkeddirectly to the accuracy of the rotational angle measuring system,leading to the following problems: firstly, such a rotational anglemeasuring system cannot be manufactured with arbitrary precision and,secondly, the registration costs increase more than proportionally withincreasing accuracy of the rotational angle measuring system.

In addition to the position errors caused by the angle measuring systemitself, there are additional translational and rotational movementerrors as a result of the mechanism of the rotational device, inparticular by the mount/guide of the parts of the rotational devicerotatable about the rotational axis, and/or movement errors, which areproduced by external forces or torques acting on the rotational axis.Forces and torques can act statically or dynamically in this case. Ingeneral, deviations from the ideal rotational movement occur in all sixdegrees of freedom (translational and rotational) in the case of themovement of parts about a rotational axis, which are subsumed by thephrase rotational error. Thus, the phrase “rotational error”, which isalso referred to as “movement error”, means all errors or deviations,such as translational and rotational deviations, which occur when partsof the rotational device rotate about a rotational axis. In the case ofmulti-stage rotational devices with a rotational movability about aplurality of rotational axes, the rotational errors in relation to onerotational axis are possibly additionally dependent on the currentrotational position of the other rotational axis (axes).

The totality of the aforementioned errors have an effect on themeasurement accuracy of the coordinate measuring machine. In particular,translational and rotational movement errors occurring at the locationof the rotational position establishment system cause errors in theestablished rotational position values, in particular angle measurementerrors.

Therefore, it is desirable to calibrate rotational devices and the anglemeasuring systems thereof. In particular, it is possible to registerrotational errors and subsequently correct or compensate these bycomputation. A specific rotational error is the so-called rotationalposition error, i.e. a deviation compared to the nominal rotationalposition value displayed by a rotational position establishment system,as already discussed above. By way of example, the rotational positionerror makes itself known by virtue of a rotational angle measuringsystem of a rotational device displaying a value deviating from theactual rotational angle. Expressed differently, the rotational positionerror is the error of the rotational position establishment system.

The aforementioned rotational errors can be registered within the scopeof a “qualification” or a computed aided accuracy (CAA) data recording.In this context, qualification means a test of assumptions, i.e. thecomparison in relation to a specification. CAA data recording denotesthe generation of a data record for the purposes of a computationalcorrection. During a CAA data recording, one or more reference pointsare set in order to be able to determine the position of measuringsensors, which are used for recording data, relative to a rotationalaxis. The relationship between measuring sensors and an axis-of-rotationcoordinate system is established with the aid of the reference points.If all translational and rotational degrees of freedom are to becorrected, the position and orientation of each individual sensorcoordinate system and the position and orientation of theaxis-of-rotation coordinate system must be known in a common inertsystem.

What is important for the qualification of rotational devices in respectof the rotational axes thereof is that the qualification takes intoaccount the conditions occurring during subsequent use. Thus, forexample, the subsequent orientation (installed position) of therotational axis may be decisive as deformations in the axis-of-rotationstructure already occur as a result of the inherent weight of therotational device. Further aspects include, for example, the used swivelregion, the weight of a measuring head to be supported, the weight of aworkpiece or torques caused by a measuring head or workpiece.Furthermore, dynamic effects may occur, for example natural dynamiceffects of the rotational axis in the form of deviations, which may becaused by different rotational speeds of a rotatable part about theaxis, or effects due to an additional movement of the rotational device,for example if the rotational device is moved along a linear axis. Theaforementioned influences require qualification taking into account theinfluences or a repetition of the qualification if the influences havechanged. For a subsequent correction, the compliance, which results in adeformation, can be established by an unloaded and/or loadedmeasurement. Here, as described in EP0684447 and DE19518268, thecompliance can contain a tilt as a result of a torque, a tilt as aresult of a force, a displacement by a torque and/or a displacement by aforce.

Against the aforementioned backdrop it is conventional to calibrate arotational angle measuring system and thus register the systematicerrors of the measuring system in order then to be able to correct orcompensate these by computation. A number of strategies or methods, suchas e.g. the spherical-plate method or rosette method, are available forregistering these systematic errors.

Although the errors can be established by these methods, thespherical-plate or rosette methods are impracticable for correcting theshort-periodic error components of the rotational angle measuring systemsince these require very much time for the aforementioned demand. Arelatively long calibration time firstly results in higher costs and,secondly, there is an increase in the negative influences as a result ofa possible temperature change during the calibration process.

Moreover, auto-calibration methods are eliminated for relatively smallrotational devices, e.g. rotary pivot joints or small rotary tables,since these require a plurality of rotational angle measuring encodersfor evaluation purposes. This space cannot be kept available inrelatively small rotational devices.

Thus, the registration of short-periodic errors of a relatively smallrotational device is not practicable to impossible for economic reasonsand reasons of accuracy using the current methods.

BRIEF SUMMARY OF THE INVENTION

An object of the present invention lies in specifying an improved methodfor establishing rotational position errors.

Different subjects of the invention are specified under the followingheadings I, II, and III, which can be combined with one another in anycombination. However, each invention subject in relation to I, II andIII also already constitutes an independent invention, wherein thesubjects in relation to II and III may solve other or further problemsthan the aforementioned problem.

I. Method for Establishing One or More Errors of a Rotational PositionEstablishment System

The aforementioned object is achieved by a method as claimed in theindependent claims. Advantageous embodiments are specified in thedependent claims.

What is specified is a method for establishing one or more errors of arotational position establishment system, which measures rotationalpositions of parts of a rotational device, in particular for acoordinate measuring machine, and/or for establishing a hysteresiseffect in such a rotational position establishment system, wherein afirst part and a second part of the rotational device are rotatablerelative to one another about a rotational axis of the rotationaldevice, and the method comprises the following steps:

-   a) establishing a first rotational position of the rotational device    with two parts rotatable relative to one another, wherein a first    rotational position of the first part is established relative to the    second part of the rotational device,-   b) establishing a first rotational position of a reference    rotational device with two parts rotatable relative to one another,    wherein one of the two parts is a third part, which, in relation to    the rotational axis, is coupled in a conjointly rotating manner to    the second part of the rotational device, and the other part of the    two parts is a fourth part, which is rotatable relative to the third    part about a rotational axis of the reference rotational device,    wherein a first rotational position of the third part is established    relative to the fourth part,-   c) as an optional step: establishing a first resultant rotational    position of the first part and of the fourth part relative to one    another in relation to the rotational axis and/or the rotational    axis of the reference rotational device, wherein the first resultant    rotational position results from the first rotational position of    the rotational device and the first rotational position of the    reference rotational device,-   d) varying the rotational position of the rotational device to a    second rotational position of the rotational device,    -   establishing the second rotational position of the rotational        device using the rotational position establishment system,    -   varying the rotational position of the reference rotational        device to a second rotational position of the reference        rotational device,    -   establishing the second rotational position of the reference        rotational device,    -   establishing a resultant rotational position of the first part        and of the fourth part relative to one another, which resultant        rotational position has been changed as a result of varying the        rotational positions,    -   establishing the rotational position error of the rotational        position establishment system from the changed resultant        rotational position of the first part and of the fourth part        relative to one another and optionally from    -   i) the rotational positions of the rotational device or the        change in the rotational position of the rotational device, and    -   ii) from the rotational positions of the reference rotational        device or the change in the rotational position of the reference        rotational device,    -   and/or, alternatively or additionally to step d),-   e) varying the rotational position of the rotational device to a    second rotational position of the rotational device and    -   varying the rotational position of the reference rotational        device to a second rotational position of the reference        rotational device    -   such that the resultant rotational position of the first part        and of the fourth part has not been changed, establishing the        second rotational position of the rotational device with the        rotational position establishment system, establishing the        second rotational position of the reference rotational device,        and    -   establishing the rotational position error of the rotational        position establishment system from the rotational positions of        the rotational device or the change in the rotational position        of the rotational device, and from the rotational positions of        the reference rotational device or the change in the rotational        position of the reference rotational device.

According to a basic concept, an error of the rotational positionestablishment system of a rotational device is established by means of areference rotational device.

According to further basic concept of the method, a rotation of parts ofthe rotational device can be counteracted by rotation of parts of thereference rotational device such that the rotational position of thefirst part and of the fourth part is not changed, or only changed alittle, even from an external observer position. This principle enablesa simplified setup for measuring the error of a rotational positionestablishment system. By way of example, the external observer positioncan be assumed by a rotational position establishment apparatus, whichis yet to be described below and which can interact with a test elementthat may be affixed to the first or the fourth part, or by a testelement. As a result of the fact that the rotational position of thefirst part and of the fourth part is not changed, or only changed alittle, from an observer position, the rotational position establishmentapparatus or the test element can remain stationary and it is possible,for example, to use rotational position establishment apparatuses whichmeasure very accurately in a small angle range.

According to the concept of this invention, the designations “firstpart”, “second part”, “third part” and “fourth part” do not set aspatial sequence of these parts or a relative arrangement of theseparts. The numbering serves for conceptually distinguishing between theparts. Furthermore, the function of the parts in a rotational device orreference rotational device is not set by the numbering. By way ofexample, the first part can be a rotor, in particular a rotary plate, ofa rotational device and the second part can be a stator, in particular alower part of a rotary table, or vice versa. Likewise, the third part,as part of the reference rotary table, can be a rotor, in particular arotary plate, and the fourth part can be a stator, or vice versa.

Denoting method steps by letters does not set a sequence in time, butserves for simpler naming and citing of method steps. If possible,method steps can be performed simultaneously or in any sequence.

When varying a rotational position, it is possible to predetermine avalue of a next, e.g. second, rotational position. Varying can beimplemented manually using an electrically or otherwise operatedactuation apparatus. An actuation apparatus can have an electroniccontrol system, e.g. a computer-assisted control system, into which anintended value of the next rotational position can be entered.

The term “establishing” describes, in general, a recognition process,specifically recognizing the rotational position in which part of arotational device or reference rotational device is relative to anotherpart of the rotational device/reference rotational device, or how largean error is. By way of example, establishing can be a visual readout,for example of a rotational position, and/or a machine readout. Areadout can be implemented, for example, on the basis of a scale and apointer, for example a scale with angle values. A readout can also beimplemented at a display. Furthermore, the establishing process can beautomated, without requiring monitoring, or separate acknowledgment, bya human. The establishing process can be a measurement process or it cancomprise one or a plurality of measurement processes, for example by anestablishment system or a measuring system. The establishing process cancomprise one or more calculations, for example if an error is intendedto be established with the aid of previously established variables.Calculations can be implemented using a computational device.

The first rotational position of the rotational device can beestablished without a rotational position establishment system, forexample in the form of a zero setting, wherein a mechanical aid, e.g. astop, may be provided for a zero setting. The first rotational positionof the rotational device is preferably established using a rotationalposition establishment system of the rotational device. Whenestablishing the first rotational position for the rotational device,the first rotational position can be set as zero position of therotational position establishment system and can be used in the furtherprocedure as zero position or reference position. If the referencerotational device also has a rotational position establishment system,it is likewise possible to set this first rotational position as zeroposition of this reference rotational position establishment system whenestablishing the first rotational position of the reference rotationaldevice and use this as zero position or reference position in thefurther procedure.

The first rotational position of the rotational device can be set or therotational device can already be in a rotational position which is usedas first rotational position of the rotational device in the method. Itis likewise possible to set the first rotational position of thereference rotational device or the reference rotational device canalready be in a rotational position which is used as first rotationalposition of the reference rotational device in the method.

A rotational position of the reference rotational device can bemeasured, for example using a rotational position establishment systemof the reference rotational device, or it may already be known withgreat accuracy. Mechanical systems for accurate relative setting ofmutually rotatable parts of a rotational device are known, for example aHirth joint.

To the extent that a rotational position measuring system is used in areference rotational device, it can already be calibrated.

A rotational position or the change in rotational position can be anangle (value) in the specific case. However, it can be specifieddifferently, for example as counters, markers or other self-selecteddimensional or dimensionless variables. An example is given bydash-shaped or other markings, which are distributed over a circularcircumference, wherein the rotational position/change in rotationalposition can be specified in this case by a number of markings such ase.g. dashes. Optionally, a conversion to an angle value can be made fromthe number of markings if the positions of the markings in relation toone another are known, in particular if distances between the markingsare known.

The method can serve different purposes. Firstly, it can be used toestablish errors of a rotational position establishment system.Secondly, it is possible to establish hysteresis effects in a rotationalposition establishment system. What this means is that the errors of therotational position establishment system can be dependent on therotational direction. Such hysteresis effects can be determined byapplying various rotational directions of the during the relativerotation of parts of the rotational device to be tested. Using themethod, it is also possible to perform error establishments a number oftimes, even when taking account of hysteresis effects, and to test areproducibility of the error establishment. Moreover a statisticalevaluation of the error data can be undertaken when establishing theerror a number of times, for example in order to establish an errordistribution. It is also possible, even in combination with theabove-described method purposes, to determine rotational position errorsat different rotational positions (or at support points yet to bedescribed below) once or a number of times, optionally in a rotationaldirection dependent manner.

In the method, two parts of the reference rotational device are rotatedrelative to one another from a first rotational position. This isreferred to as “varying the rotational position of the referencerotational device” or “setting the rotational position of the referencerotational device”. The changed rotational position or the change in therotational position of these two parts can be measured accurately, forexample by means of a very accurate, optionally calibrated rotationalposition measuring system that is integrated into the referencerotational device. By way of example, an angle, about which the twoparts of the reference rotational device are rotated relative to oneanother, is known accurately in this manner. The reference rotationaldevice is preferably a calibrated or a self-calibrating rotationaldevice, in particular a self-calibrating rotary table. Aself-calibrating rotational device is disclosed in the document“Calibration of angle encoders using transfer functions” by Geckeler,R.; Fricke, A.; Elster C. in Measurement Science and Technology volume17 (2006). The changed rotational position or the change in therotational position for the reference rotational device can otherwisealso be known accurately or be adjustable without using a rotationalposition measuring system, for example due to a very accurate mechanicalactuation device such as e.g. a Hirth joint.

By way of example, the term “accurate” means that the rotationalposition measuring system of the reference rotational device has asmaller error than the rotational position measuring system of therotational device, the error of which is intended to be established, orthat an actuation device has a smaller error then the rotationalposition measuring system of the rotational device. Preferably, theerror of the rotational position measuring system or actuation system ina reference rotational device is less than or equal to ½ the error ofthe rotational position measuring system of the rotational device, morepreferably less than or equal to ⅕, most preferably less than or equalto 1/10.

A rotational device has a rotational movability of a first part and asecond part about at least one rotational axis, wherein the first partand the second part are rotatably movable relative to one another due tothe rotational movability of the rotational device and wherein the firstor the second part is configured to hold e.g. either a workpiece or atactile measuring head, e.g. with a sensing unit, or a general sensor inorder to enable a rotation of the workpiece or of the measuring head orsensor. Rotational devices which have rotational movabilities about tworotational axes (e.g. a so-called rotary pivot joint with two rotationalaxes which extend perpendicular to one another) or about more than tworotational axes are also utilizable.

In one embodiment, the first or the second part of the rotational deviceis configured to hold a workpiece. The other part is configured, inparticular, to be fastened to a base of a CMM and/or to be positioned ona base such that this part is immovable relative to the base while theother part can be rotated relative to the base.

In accordance with a further embodiment of the arrangement, the first orthe second part of the rotational device is configured to hold a tactilemeasuring head, e.g. with a sensing unit or, in general, a sensor. Inthis case, the first and the second part enable a rotation of themeasuring head or of the sensor by way of a relative movement. By way ofexample, so called rotary pivot joints, which enable a rotationalmobility in relation to two rotational axes, which extend transverselyand, in particular, perpendicular to one another, are known. However,the rotational devices which merely enable a rotational movability inrespect to a single rotational axis or which enable rotations about morethan two rotational axes are also known.

Examples for rotational devices where an error is intended to beestablished in the rotational position establishment system thereof arerotary joints, rotational devices with a plurality of rotational axes,rotary pivot joints, which have a plurality of rotational axes, rotarytables and rotary pivot tables. The invention relates, in particular, torotational devices which are utilizable in coordinate measuring machines(abbreviated as CMM below), machine tools, robots and otherapplications, in which high accuracy is important. The rotational deviceis also referred to as test object.

The rotational device and the reference rotational device can haveself-driven rotational axes, can be manually or semi-automaticallyimplementable rotary joints, e.g. rotary joints implementable inreproducible three-point bearings. The (reference) rotational device canalso be a partial apparatus, i.e. a component of a superordinate devicesuch as a machine tool.

In the method, two parts of the rotational device, at which therotational position error is intended to be determined by the rotationalposition establishment system thereof, are rotated relative to oneanother out of the first rotational position. This is referred to as“varying the rotational position of the rotational device”. The changedrotational position or the change in rotational position of these twoparts relative to one another is not known accurately as a result of therotational position error of the rotational position establishmentsystem which is still unknown and to be determined by the method.

One of the parts of the rotational device is coupled in a conjointlyrotating manner to one of the parts of the reference rotational device(e.g. second and third part as specified above).

The remaining parts (first and fourth part as specified above) of therotational device and of the reference rotational device can likewise beconjointly rotating in relation to one another or be rotatable relativeto one another.

Step c) of the method specified above is an optional step which is notrequired if the first and the fourth part are not rotatable relative toone another. In this case, establishing a first resultant rotationalposition of the first part and of the fourth part relative to oneanother can be dispensed with, since these parts are not rotatable inrelation to one another in any case and consequently the position ofboth parts in relation to one another is known from the outset. However,no harm is done by once again determining the rotational position. Thefirst and the fourth part can be coupled to one another in a conjointlyrotating manner, for example by mechanical coupling means such assupports, connectors etc. If the first and the fourth part areconjointly rotating in relation to one another, the first and the fourthpart are rotated together and by the same amount about parts two andthree, which are likewise coupled to one another in a conjointlyrotating manner. Varying the rotational position of the rotationaldevice and varying the rotational position of the reference rotationaldevice in this variant result in the first and the fourth parts keepingan unchanged rotational position relative to one another, as specifiedin the alternative in step e).

If the first part and the fourth part are rotatable relative to oneanother, varying the rotational position of the rotational device andvarying the rotational position of the reference rotational device haveas a consequence that either the first and the fourth part assume aresultant rotational position relative to one another which has changedin comparison to what was previously, as specified in the alternative instep d), or that they assume an unchanged rotational position relativeto one another, as specified in the alternative in step e). Bothalternatives will be described in more detail below.

Method in Accordance with Step d)

The resultant rotational position, changed relative to one another, ofthe first part and of the fourth part is established. During theestablishment, the initial position (prior to varying the rotationalpositions) and the changed rotational position (after varying therotational positions) can be established or measured, from which thechange can be established, or there can be a direct establishment of thechange. The establishment of the change means that a change value (e.g.change in angle) is established directly as a difference between twovalues (e.g. discrete angle values).

A changed resultant rotational position of the first part and of thefourth part relative to one another is established very accurately, forexample by means of a further measuring system, preferably by means of arotational position establishment apparatus, in particular an angleestablishment apparatus, as will still be described below.

As a further variable, the changed rotational position or the change inthe rotational position of the two parts of the reference rotationaldevice (third and fourth parts) relative to one another is knownaccurately or measured accurately, for example by means of an accuraterotational position measuring system present in the reference rotationaldevice, in particular by means of a rotational angle measuring system.

The following settings or variables are known:

-   i. the changed rotational position of the rotational device, i.e.    changed rotational position of the first and the second part    relative to one another, displayed by the rotational position    establishment system, the error of which is intended to be    determined, for example an angle (change) value,-   ii. the changed rotational position of the reference rotational    device, i.e. changed rotational position of the third and fourth    parts relative to one another, which is known accurately or    established accurately, for example an angle (change) value,-   iii. the changed rotational position of the first and the fourth    part relative to one another, which is known accurately, for example    an angle (change) value.

Using iii) and optionally also using i) and ii), it is possible toestablish the error of the rotational position establishment system, asexplained on the basis of an exemplary embodiment. Thesettings/variables i) and ii) are not required in all cases. By way ofexample, if the changed rotational position of the rotational devicecorresponds to a displayed, error-afflicted (angle) value and if thechanged rotational position of the reference rotational devicecorresponds to a negated (angle) value in respect thereof—expresseddifferently: if the two (angle) values have an equal magnitude butopposite sign, with the (angle) value of the rotational device beingerror afflicted—then the error can be determined merely from iii), asspecified in the exemplary embodiments. If the aforementioned (angle)values, i.e. the value for i) and the value for ii), are unequal interms of magnitude and/or do not have an opposite sign, then i) and ii)are also used for establishing the error.

Values which are

-   I. displayed by the error-afflicted rotational position    establishment system of the rotational device or-   II. displayed by the rotational position establishment system of the    reference rotational device or set at the reference rotational    device    are also referred to as “nominal values” in this invention.

In I. (rotational device), the nominal value deviates from the realvalue by the magnitude of the error to be established. In principle,this is also the case in II. (reference rotational device). However, thereference rotational device is more accurate, with reference being madeto the definition of accuracy provided above. In this invention, thenominal value of the reference rotational device is preferably assumedto be a real value and establishments are made on the basis thereof.

Method in Accordance with Step e):

What is determined in the alternative of step e) is that the resultantrotational position of the first part and of the fourth part isunchanged. An unchanged resultant rotational position of the first partand of the fourth part relative to one another is establishedaccurately, for example by means of a further measuring system,preferably by means of a rotational position establishment apparatus,preferably a rotational angle establishment apparatus, as will still beexplained below.

The following settings or variables are known:

-   i. the changed rotational position of the reference rotational    device, i.e. changed rotational position of the third and fourth    parts relative to one another, which is known accurately, for    example an angle (change) value,-   ii. the changed rotational position of the rotational device, i.e.    changed rotational position of the first and second parts relative    to one another, displayed by the rotational position establishment    system, the error of which is intended to be determined,    and it is furthermore known that the unchanged rotational position    of the first and fourth parts relative to one another is unchanged.

Using i) and ii), it is possible to establish the error of therotational position establishment system, as explained on the basis ofan exemplary embodiment.

In the method, steps d) can be performed a number of times or steps e)can be performed a number of times. A number of variations of therotational position of the rotational device and/or of the rotationalposition of the reference rotational device are preferably undertaken,i.e. a plurality of changed rotational positions of the rotationaldevice and/or reference rotational device are set. By way of example,the rotational position of the rotational device/reference rotationaldevice can be varied from the second rotational position to a thirdrotational position, from the third rotational position to a fourth one,etc. In the plurality of variations, the rotational directions can varyin the rotational device and/or the reference rotational device.

It is likewise possible to perform steps d) and e) respectively once ora number of times. A number of variations of the rotational position ofthe rotational device and/or of the rotational position of the referencerotational device are preferably undertaken, i.e. a number of changedrotational positions of the rotational device and/or referencerotational device are set.

For performing steps d) and/or e) a number of times, a plurality ofrotational positions can be set for the reference rotational deviceand/or the rotational device, which are also referred to as “supportpoints” for registering rotational position errors.

Such support points can be distributed irregularly or regularly on oneor more relative rotations of the parts of the reference rotationaldevice and/or rotational device. An integer divisor of 360° ispreferably selected as a distance between the support points(increment). The number of support points can be increased arbitrarily,or the increment can be reduced arbitrarily, as a result of whichshort-periodic errors in particular can be registered and aliasingeffects, which are generated by an increment that is too large, can bereduced or avoided.

Both the positioning of the rotational axes and data evaluation ispossible in a very quick and accurate manner using the method.Therefore, the method has, in particular, the following advantages:

-   -   A very fast rotational position error registration is possible,        even in the case of a large number of support points. This        enables the following:    -   A practicable registration of short-periodic errors of the        rotational position establishment system. By way of example, if        use is made of a self-calibrating reference rotational device,        it is possible to obtain constant monitoring regarding the        accuracy of the reference rotational device, and hence regarding        the accuracy of the error establishment.    -   Calibration costs are saved when using a self-calibrating        reference rotational device.    -   Registration of rotational position errors is possible in a        multiplicity of rotational devices, e.g. also in the case of        latching rotary pivot joints or rotational devices which, as a        result of the design thereof, only have limited space for sensor        systems.    -   The registration of the rotational position errors can be        implemented in the finished overall system. That is to say,        possible bracing of the scale as a result of assembly thereof is        also taken into account; if forces act on the scale (e.g.        tensions generated by adhesive bonding), the latter deforms. By        way of example, the scale is a graduated disk, in which        deformations cause a change in the division spacing.    -   If required, accurate registration of the rotational position        errors in portions of the rotational position establishment        system is possible.

Coupling between rotational device and reference rotational device canbe implemented in various ways:

Both devices can be positioned directly joining one another. Thecoupling can be implemented, in particular, by a force fit or in aninterlocking manner. By way of example, coupling can be implemented byfrictional forces, for example if the reference rotational device andthe rotational device are positioned on one another and the weight ofone of the devices weighs on the other device.

A bearing can be provided between the reference rotational device andthe rotational device, for example a three-point bearing.

One or more holding elements or adapters can be arranged between therotational device and the reference rotational device. A specificholding element will still be described in this description and in theexemplary embodiments.

The coupling between rotational device and reference rotational deviceis preferably such that the rotational axis of the rotational device(axis about which the parts of the rotational device rotate relative toone another) and the rotational axis of the reference rotational device(axis about which the parts of the reference rotational device rotaterelative to one another) are coaxial or axially flush or substantiallycoaxial or substantially axially flush in relation to one another.

In one embodiment of the method, the rotational position of the firstpart and of the fourth part relative to one another, i.e. the unchangedrotational position of the two parts relative to one another or thechange in the rotational position of the two parts relative to oneanother, is determined with the aid of a rotational positionestablishment apparatus. In accordance with step d) of the method above,a changed resultant rotational position of the first part and of thefourth part relative to one another can be determined by means of therotational position establishment apparatus. Alternatively oradditionally, in accordance with step e) of the method above, therotational position establishment apparatus can be used to determinethat the rotational positions of the first part and of the fourth partrelative to one another are unchanged. In these embodiments (d) & e)),the rotational position establishment apparatus serves as a highlyaccurate additional measuring system. By way of example, establishingthe error of the rotational angle measuring system to be calibrated isimplemented in this case by comparing a rotational angle measuringsystem of the reference rotational device with the (error-afflicted)rotational angle measuring system of the rotational device, wherein therotational position establishment apparatus serves as further measuringsystem. A calculation principle is specified in the examples.

An example of a rotational position establishment apparatus is an anglemeasuring apparatus. A specific example of a rotational positionestablishment apparatus in an autocollimator or an arrangement of aplurality of autocollimators. In a different variant, one or moredistance sensors, such as e.g. laser rangefinders, laserinterferometers, capacitive distance sensors, magnetoresistive distancesensors, magnetoresistive angle sensors, can be used as a rotationalposition establishment apparatus. These rotational positionestablishment apparatuses can be combined with one another and/or it ispossible to use a plurality of apparatuses of the same type. Instead ofmeasuring angles, or in addition to measuring angles, rangefinders ordistance sensors can also be used for establishing translationalmovement errors. Specific arrangements of rotational positionestablishment apparatuses are described in the exemplary embodiments.

It is also possible to use a coordinate measuring machine as arotational position establishment apparatus.

When using a rotational position establishment apparatus, the rotationalposition of the first part and of the fourth part relative to oneanother is preferably established with the aid of a test element,wherein the rotational position or change in rotational position of thetest element relative to the rotational position establishment apparatusor relative to another reference point is established by means of therotational position establishment apparatus.

In particular, the positioning of the rotational position establishmentapparatus and test element can be as follows:

-   -   the rotational position establishment apparatus is positioned in        relation to the first part or the fourth part, for example        coupled to the first part or to the fourth part, in such a way        that it is conjointly rotating in relation to the first part or        the fourth part,    -   the test element is positioned in relation to the first part or        the fourth part, for example coupled to the first part or to the        fourth part, in such a way that it is conjointly rotating in        relation to the first part or the fourth part,        wherein the rotational position establishment apparatus is        conjointly rotating in relation to the first part if the test        element is conjointly rotating in relation to the fourth part,        and the rotational position establishment apparatus is        conjointly rotating in relation to the fourth part if the test        element is conjointly rotating in relation to the first part.

In the above context, the phrase “conjointly rotating” means, inparticular, conjoint rotation in respect of a rotation about therotational axis of the rotational device or the rotational axis of thereference rotational device. Conjoint rotation in relation to thefirst/fourth part means that the rotational position establishmentapparatus or the test element co-rotates with the first/fourth partabout the same rotational angle, or any other scale unit, when thefirst/fourth part is rotated.

A conjointly rotating arrangement relative to the first or fourth partcan be designed in many various ways. By way of example, a coupling ofthe rotational position establishment apparatus or of the test elementto the first of fourth part can be implemented. A coupling can containarbitrarily many intermediate elements.

In one variant, the rotational position establishment apparatus and/orthe test element is/are attached to the rotational device or to thereference rotational device. If the first of fourth part is e.g. a rotorof a (reference) rotary table, then the rotational positionestablishment apparatus or the test element can be attached directly orindirectly to the rotor, e.g. a rotary plate, and co-rotate with therotor. The respective other part, i.e. the fourth part if the first partis the aforementioned rotor, can then be positioned in a non-rotatablemanner on a substrate or on a stationary support and either therotational position establishment apparatus or the test element canlikewise be positioned on the substrate or on the support such that itis conjointly rotating in relation to the first part. In this case, thesubstrate can be considered to be a coupling element. In anothervariant, both parts (first and fourth parts) can be rotatable inrelation to a substrate. Various variants are presented in the exemplaryembodiments.

The rotational position of the first part and of the fourth partrelative to one another can be determined with the aid of the relativerotational position of the rotational position establishment apparatusand of the test element, which can be changed or unchanged after varyingthe rotational positions of the rotational device and referencerotational device. It is possible to determine either the change in therotational position of the first part and of the fourth part relative toone another or it is possible to determine the unchanged rotationalposition of the two parts relative to one another.

An unchanged position of the first part and of the fourth part relativeto one another can be produced in such a way that the rotationalposition of the test element or of the rotational position establishmentapparatus is set in such a way in accordance with the above-describedvariant e) that an unchanged relative position of the test element isdetermined with the rotational position establishment apparatus. This isalso referred to as tuning to an unchanged position or as tuning to thezero deviation. The terms “unchanged position” and “zero deviation”should be considered in the context of the measurement accuracy/errormargin of the rotational position establishment apparatus and in thecontext of the manual or machine adjustment accuracy of the rotatableparts of the rotational device and reference rotational device, i.e. anunchanged position or a zero deviation can only be achieved within thescope of the measuring accuracy and adjustment accuracy. For the method,an autocollimator is particularly suitable as a rotational positionestablishment apparatus and a mirror is particularly suitable as a testelement.

In one variant, the test element is a reflector, wherein the directionof radiation which is reflected by the reflector is dependent on therelative rotational position between the first part and the fourth part.The reflector is likewise rotated during a change in the rotationalposition of the first part in relation to the fourth part. A reflectorcan be used, in particular, if the rotational position establishmentapparatus is an autocollimator or a laser distance sensor. An exemplaryreflector is a mirror, in particular a plane mirror, or aretroreflector. A measurement beam is transmitted to the reflector, theformer being reflected by the reflector.

In a further variant, the test element is a measurement body which isarranged at a distance from the rotational axis and/or in a manner notcoaxial with the rotational axis such that the rotational angle of themeasurement body about the axis is determinable by the measuring deviceon the basis of a changed rotational position of the measurement body.The phrase “at a distance from the rotational axis” means that therotational axis does not intersect the measurement body. In thisdescription, the phrase “(not) coaxial” is synonymous with “(not)concentric”. Not coaxial means that a rotational symmetry axis oranother symmetry axis of the measurement body, for example of a sphere,is not coaxial (or expressed differently: not flush) with the rotationalaxis.

A measurement body as a first test element, which is arranged at adistance from the rotational axis and/or in a manner not coaxial withthe rotational axis, may be any body at which a uniquely definedcoordinate system can be determined. Examples include a sphere, a triplesphere, a cylinder, a triple sphere, a cone, a prism or any othergeometric body. In particular, the measurement body has one or morereference points, also referred to as “points in space”, which aredeterminable by a measuring system of the CMM, such that the rotationalposition is determinable by determining the position of the referencepoint or points in various rotational positions of the measurement body.In principle, any measurement body, at or in which a reference point ora point in space is uniquely determinable using the measuring system ofa CMM, can be used.

By way of example, the reference point can be determined by probingusing a sensing system of a CMM. If the test element is a sphere, thene.g. the sphere center can be used as reference point, the position ofwhich can be determined by multiple probing of the sphere surface. Byway of example, the rotational device is a rotary table and a spherewhich is positioned laterally from the rotary table axis is used as atest element. In a first angle position, the position of the sphere andof the sphere center can be registered using the measuring system of theCMM, e.g. by way of sensing. After rotating the rotary table plate intoa second position, the changed sphere position and the sphere center canbe registered anew and the rotational angle of the rotary table platecan be established from the measured values. At the different spherepositions, the sphere center is preferably determined by multipleprobing.

Possibly present form defects of the measurement body can be calibratedin a separate step and the error can be taken into account when themeasurement body is used. This can be dispensed with if the same orsubstantially the same surface points are always measured on themeasurement body, for example using the sensing system of a CMM.

When varying the rotational position of the rotational device and therotational position of the reference rotational device, the first partcan be rotated in a first direction against the second part in therotational device and the third part can be rotated in the samedirection against the fourth part in the reference rotational device. Inthe case of the same observation position or field of view, it ispossible, for example, for the first part to be rotated clockwise(positive rotational direction) against the second part in therotational device and the third part can likewise be rotated clockwiseagainst the fourth part in the reference rotational device. Analogously,the rotation can respectively be implemented in a counterclockwisemanner (negative rotational direction). In the case of a rotation, theterms “co-rotating” or “same direction” and “counter rotating” or“opposite direction” generally assume the same observation position orfield of view, i.e. the same observation position of an external,stationary observer, wherein the observation position of the external,stationary observer is also referred to as “inert system”.

By way of example, this variant can be applied if two or morereflectors, in particular plane or substantially plane mirrors, are usedas test elements. Two or more reflectors are also referred to asreflector arrangement.

By way of example, two reflectors or reflector layers can be present inthe reflector arrangement, which reflectors are at an angle of >180° to360° in relation to one another. The angle between two reflectors orreflector layers is measured from the reflecting surface of onereflector or one reflector layer to the reflecting surface of anotherreflector or another reflector layer. In the case of an angle of 360°,the reflectors/reflector layers point in opposite spatial directions.

By way of example, more than two reflectors or reflector layers bepresent in a reflector arrangement, which reflectors or reflector layersare at an angle in relation to one another and point in various spatialdirections, wherein adjacent reflectors or reflector layers arepreferably at an angle of >180° to <360° in relation to one another,wherein the angle is defined as in the case above. In a specificpreferred variant, neighboring reflectors or reflector layers can be atan angle ofα=360°−[(N−2)/N]*180°in relation to one another, where N is an integer greater than or equalto 3. By way of example, the reflectors can be applied to the side facesof a prism, the base area of which forms a regular N-gon. A rotation isthen preferably implemented in such a way that the first part is rotatedagainst the second part by ½*360°/N in a first direction and, in thereference rotational device, the third part is rotated against thefourth part by ½*360°/N in the same direction.

In another embodiment, the first part is rotated in a first directionagainst the second part in the rotational device and the third part isrotated in the opposite direction thereto against the fourth part in thereference rotational device when varying the rotational position of therotational device and the rotational position of the referencerotational device. Here, the same observation position is assumed, i.e.the same observation position of an external, stationary observer,wherein the observation position of the external, stationary observer isalso referred to as “inert system”. In the case of the same observationposition, it is possible, for example, for the first part to be rotatedclockwise against the second part in the rotational device and the thirdpart to be rotated counterclockwise against the fourth part in thereference rotational device. In one variant of this embodiment, parts ofthe rotational device are rotated relative to one another by the samemagnitude, e.g. angle magnitude or counter magnitude, as parts of thereference rotational device are rotated relative to one another. Themagnitude of the rotation at the rotational device is set on the basisof the rotational position establishment system of the rotational deviceor displayed thereby and it is a nominal magnitude. In a further variantof this embodiment, parts of the rotational device are rotated relativeto one another and parts of the reference rotational device are rotatedrelative to one another in such a way that the rotational position ofthe first part and of the fourth part is unchanged relative to oneanother in comparison with the state prior to the rotations. As alreadymentioned above, the term “unchanged” means a non-change within thescope of the measurement accuracy and setting accuracy, for examplewithin the scope of the measurement accuracy of an autocollimator asrotational position establishment apparatus. An “unchanged position”within the scope of the measurement accuracy and setting accuracy canalso be referred to as “substantially unchanged position”.

In a preferred method variant, at least one variation of the rotationalposition of the rotational device is undertaken in the positiverotational direction and at least one variation of the rotationalposition of the rotational device is undertaken in the negativerotational direction. This method variant is advantageous foridentifying hysteresis effects. The type of bearing of mutuallyrotatable parts, e.g. an air bearing or a roller bearing, is frequentlythe largest influencing factor for a hysteresis. Furthermore, therotational position establishment system of the rotational device andthe rotational position establishment system of the reference rotationaldevice can cause a hysteresis.

If the rotation of the parts is undertaken in such a way that, aftervarying the rotational positions, the position of the first part to thefourth part relative to one another is unchanged, then the variation ofthe rotational position of the rotational device is compensated for bythe variation of the rotational position of the reference rotationaldevice. That is to say that a variation in the rotational position ofthe first part in relation to the fourth part, which is caused by avariation of the rotational position of the rotational device, iscompensated for, expressed differently: lifted again, by a variation ofthe rotational position of the reference rotational device. Or, that avariation in the rotational position of the first part in relation tothe fourth part, which is caused by a variation of the rotationalposition of the reference rotational device, is compensated for,expressed differently: lifted again, by a variation of the rotationalposition of the rotational device. Here, and in the method in general,it is irrelevant whether the rotational position of the rotationaldevice is varied first, followed by the rotational position of thereference rotational device, or vice versa, or whether both variationsare implemented simultaneously.

In one embodiment, the method comprises the following steps: performingthe method with steps a)-d) and/or e), as described above, andfurthermore:

-   -   f) restoring the first rotational position of the rotational        device, corresponding to the first rotational position in step        a), or substantially to such a rotational position, or restoring        the first rotational position of the reference rotational        device, corresponding to the first rotational position in step        b), or substantially to such a rotational position,    -   g) producing a modified first rotational position of the        reference rotational device when the rotational device was        brought into the first rotational position from step a), or        producing a modified first rotational position of the rotational        device when the reference rotational device was brought into the        first rotational position from step b),        -   such that, in the modified first rotational position of the            rotational device/reference rotational device, there is a            modified rotational position of the first part and of the            fourth part relative to one another,        -   wherein the fourth part is twisted relative to the first            part by an angle value, preferably by 360°/M, compared to            the first resultant rotational position of the first part            and of the fourth part relative to one another in step c),            wherein M is an integer, preferably greater than or equal to            2, more preferably 2 to 8,    -   h) performing the method steps d) and/or e), optionally also        step c), as described above, proceeding from the first or        substantially the first rotational position of the rotational        device and the modified first rotational position of the        reference rotational device, or proceeding from the first or        substantially the first rotational position of the reference        rotational device and the modified first rotational position of        the rotational device.

The above method is also referred to as “flipping-over method” in thisinvention, not only for the special case M=2. In the case of suchrepetition of method steps d) and/or e) within the scope of the aboveembodiment with steps f)-h), residual errors of the rotational positionestablishment can be compensated for, which residual errors can becaused, for example, by the type of method setup, the arrangement ofutilized components or systematic residual errors of a rotationalposition establishment apparatus of the reference rotational device.

Steps d) and/or e) can be performed a number of times in step h) of themethod variant above and various rotational positions can be produced.Step c) can be performed optionally in order to verify the desiredresultant rotational position of the first part and of the fourth partrelative to one another, i.e. to verify whether the fourth part istwisted relative to the first part by an angle value of 360°/M in themodified rotational position, as specified in step g). Step c)preferably also serves for establishing a start position of the method.If a mirror is used as test element and an autocollimator is used asrotational position establishment apparatus, it is advantageous toperform step c) in order to determine an offset of a test element, whichwill still be explained below.

After performing the above-described steps, it is still possible to setone or more further, modified first rotational positions of therotational device and/or of the reference rotational device and toperform method steps d) and/or e), and optionally also step c), againproceeding therefrom.

Preferably, the method with steps f)-h) is performed (M−1) times,wherein there is a twist about an angle value of 360°/M in step g) eachtime it is performed. By way of example, if M=3, it is possible,initially, to perform the method described at the outset with stepsa)-e) and then perform the sequence of steps f)-h) (M−1) times, i.e.twice. When the sequence of steps f)-h) is performed the first time, afirst modified resultant rotational position of the fourth part relativeto the first part is produced in the process, in which the fourth partis twisted relative to the first part by an angle value of 360°/3 (M=3)compared to the first resultant rotational position of the first partand of the fourth part relative to one another in step c). When thesequence of steps f)-h) is performed the second time, a second modifiedresultant rotational position of the fourth part relative to the firstpart is produced in the process, in which the fourth part is twistedrelative to the first part by an angle value of 360°/3 compared to thefirst modified resultant rotational position from the first performanceof the sequence of steps f)-h). In the case of another twist by 360°/3,the fourth part relative to the first part would once again reach theresultant rotational position from step c), which is why this step and arenewed performance of the method are unnecessary as the method wasalready performed from this resultant rotational position. Analogouslyto the example above, the sequence of steps f)-h) can respectively beperformed (M−1) times for M=4, 5 or 6 and the resultant (modified)rotational positions of the first and of the fourth parts with respectto one another are respectively changed by 360°/4, 360°/5 or 360°/6.

In a further aspect, the invention relates to an arrangement forestablishing errors of a rotational position establishment system whichmeasures rotational positions of parts of a rotational device for acoordinate measuring machine, particularly for performing theaforementioned method, wherein the arrangement comprises:

-   -   the rotational device, which has a first part and a second part,        which are rotatable relative to one another about a rotational        axis of the rotational device,    -   the rotational position establishment system,    -   a reference rotational device comprising two parts rotatable        relative to one another, wherein one of the two parts is a third        part, which, in relation to the rotational axis, is coupled in a        conjointly rotating manner to the second part of the rotational        device, and the other part of the two parts is a fourth part,        which is rotatable relative to the third part about a rotational        axis of the reference rotational device, wherein the rotational        axis of the reference rotational device is preferably coaxial or        substantially coaxial with the rotational axis of the rotational        device,    -   a rotational position establishment apparatus for establishing a        resultant rotational position of the first part and of the        fourth part relative to one another in relation to the        rotational axis,    -   an error establishment apparatus for establishing the error of        the rotational position establishment system, wherein the        establishment apparatus is configured to establish the        rotational position error of the rotational position        establishment system        -   from the changed resultant rotational position of the first            part and of the fourth part relative to one another, and            optionally from        -   i) the rotational positions of the rotational device or the            change in the rotational position of the rotational device,            and        -   ii) from the rotational positions of the reference            rotational device or the change in the rotational position            of the reference rotational device, and/or, alternatively or            additionally,        -   from the rotational positions of the rotational device or            the change in the rotational position of the rotational            device, and from the rotational positions of the reference            rotational device or the change in the rotational position            of the reference rotational device.

In respect of the arrangement and the components of the arrangement,reference is made to the above disclosure of the method, whereinembodiments of the arrangement for performing the method are alreadydisclosed.

Examples of a rotational position establishment apparatus were alreadymentioned above. It is also possible to use a coordinate measuringmachine as a rotational position establishment apparatus. In a furthervariant, one or more distance sensors can be used as rotational positionestablishment apparatus.

In the aforementioned arrangement a test element is preferably attachedto the rotational device and/or to the reference rotational device, therotational position or change in rotational position of which testelement is registered using the rotational position establishmentapparatus. The test element is preferably attached to the first part orto the fourth part. In one variant, the test element is a reflectorwhich reflects radiation incident thereon dependent on the relativerotational position of the first part in relation to the fourth part. Areflector can be used, in particular, if the rotational positionestablishment apparatus is an autocollimator or a laser distance sensor.An exemplary reflector is a mirror or a retroreflector.

In a further variant, the test element is an already describedmeasurement body, which is arranged at a distance from the rotationalaxis and/or in a manner not coaxial with the rotational axis such thatthe rotational angle of the measurement body about the axis isdeterminable by the measuring device on the basis of a changedrotational position of the measurement body.

II. Test Body, Arrangement with the Test Body and Method Using the TestBody

In a further aspect, the invention relates to a test body which, inparticular, can be used for performing the above-described method. Thetest body has a test element which was already mentioned above.Furthermore, the test body can also be used to establish furtherrotational errors, as described in the exemplary embodiments. Using thetest body, it is possible to establish rotational errors of a rotationaldevice with high precision and with the shortest possible time outlay.

What is specified is a test body for establishing one or more rotationalerrors of a rotational device, in particular of a rotational device fora coordinate measuring machine, in respect of one or more degrees offreedom of movement, in which a real rotational movement of therotational device differs from an ideal rotational movement, wherein thetest body comprises:

-   -   a holder, which is rotatable together with part of the        rotational device about a rotational axis and which is embodied        to arrange or fasten the test body in relation to the rotational        axis about which the test body is to be rotated for establishing        the rotational errors,    -   a test element rigidly connected to the holder or formed on the        holder, wherein the test element serves to establish the        rotational error in respect of one or more of the degrees of        freedom of movement,        wherein the test element is a reflector which is aligned at an        angle to the rotational axis and reflects radiation incident        thereon in a direction dependent on the rotational angle of the        test body, or wherein the test element is a measurement body        which is arranged at a distance from the rotational axis and/or        in a manner not coaxial with the rotational axis such that the        rotational angle of the test body is determinable by an        associated sensor or by the measuring system of a coordinate        measuring machine on the basis of the rotational position of the        test element. Such a test body is combinable in any combination        with one or more of the subjects of the invention, embodiments        and variants described in this description.

Also specified is a test body for establishing one or more rotationalerrors of a rotational device, in particular of a rotational device fora coordinate measuring machine, in respect of one or more degrees offreedom of movement, in which a real rotational movement of therotational device differs from an ideal rotational movement, wherein thetest body comprises:

-   -   a holder, which is rotatable together with part of the        rotational device about a rotational axis and which is embodied        to arrange or fasten the test body in relation to the rotational        axis about which the test body is to be rotated for establishing        the rotational error or rotational errors,    -   a plurality of test elements rigidly connected to the holder or        formed on the holder, wherein each one of the test elements        serves to establish the rotational error in respect of one or        more of the degrees of freedom of movement,        wherein a first one of the test elements is a reflector which is        aligned or alignable at an angle to the rotational axis and        reflects radiation incident thereon in a direction dependent on        the rotational angle of the test body, or        wherein a first one of the test elements is a first measurement        body which is arranged, or can be arranged, at a distance from        the rotational axis and/or in a manner not coaxial with the        rotational axis such that the rotational angle of the test body        is determinable by an associated sensor or by the measuring        system of a coordinate measuring machine on the basis of the        rotational position of the test element,        wherein a second one of the test elements is a reflector which        is aligned or alignable at an angle to the rotational axis and        which reflects radiation incident thereon in a direction        dependent on the rotational angle of the test body and which, if        another reflector which is a test element of the test body is        present, is aligned in a different direction to the other        reflector and which, if another reflector which is a first test        element of the test body is present, can be attached together        with the other reflector at a common support body, or        wherein a second one of the test elements is a reflector which        is aligned in the direction of the rotational axis and which, if        another reflector which is a first test element of the test body        is present, can be attached together with the other reflector at        a common support body, or        wherein a second one of the test elements is a second        measurement body which is a rotationally symmetric measurement        body or which has a face pointing in one direction or a        plurality of faces pointing in different directions. What        applies to one or more faces is that they are preferably a        planar or substantially planar face, or that they are a planar        face in at least a portion of the face.

The phrase “rotational error” comprises all translational and rotationaldeviations which occur during the operation of the rotational device, inparticular three translational errors in respect of the Cartesiancoordinate axes X, Y and Z, referred to as Tx, Ty, Tz, and rotationalerrors in respect of the Cartesian coordinate axes X, Y, referred to asRx, Ry, provided that the rotational axis of the rotational device isaligned in the Z-direction (more in this respect is outlined below). Ifthe movement about the rotational axis were an ideal rotationalmovement, there would be no rotational errors. This applies within thescope of the measurement accuracy of the sensors which are used incombination with the test elements and within the scope of the precisionwith which the test body is manufactured (e.g. precision of therotational symmetry of a measurement body and precision of a mirror as atest element). In particular, the test body can be calibrated in advancein combination with the assigned sensors in order to correct oreliminate measurement errors of the sensors and deviations from theideal design of the test body.

A specific rotational error is the rotational position error which wasalready mentioned and defined above. To the extent that the rotationalaxis is aligned in the Z-direction of a Cartesian coordinate system, therotational position error in this invention is also referred to as Rz.Naturally, different alignments of the rotational axis in a differentdirection of the Cartesian coordinate system are possible, e.g. ahorizontal alignment. In the case of an alignment of the rotational axisin the Y-direction of a predetermined coordinate system, the rotationalposition error would be referred to as Ry; in the case of an alignmentin the X-direction, it would be referred to as Rx. In the selectedexample, Rz should be distinguished from Ry and Rx to the extent that,here, the rotation of the rotatable part of the rotational device aboutthe rotational axis aligned in the Z-direction is desired in therotational device, whereas a rotation of the rotatable part about adifferent spatial axis—X or Y—is undesired and constitutes a deviationfrom the ideal rotational movement.

Examples of rotational devices are rotary joints, rotary pivot joints,which have a plurality of rotational axes, and rotary tables. Theinvention relates in particular to rotational devices which are usablein coordinate measuring machines (abbreviated to CMM below), machinetools, robots and other applications in which high accuracy isimportant. The rotational device is also referred to as test object.

A rotation of the test body is implemented by virtue of it beingarranged at or on the rotational device and co-rotated when therotational device is rotated. The rotational device preferably has afirst and a second part which are rotatable relative to one another. Thetest body is preferably fastened on or at one of the rotatable parts ofthe device in such a way that it is not rotatable relative to this part.Thus, if, for example, the test body is arranged at a second part of therotational device and if the second part is rotated relative to thefirst part, the test body is also rotated about the same rotationalangle relative to the first part as the second part. By way of example,the test body can be positioned on the plate of a rotary table to bequalified, or at a rotatable part of a rotary pivot joint.

The fact that the holder, and hence the test body, are rotatable about arotational axis does not imply a rotational movability of the holder ortest body when considered on its own. Rather, the test body isconfigured for a rotation about a rotational axis if it is arranged in apredetermined manner, preferably in a reproducible manner, at arotational device or at a reference rotational device which will stillbe described below. The phrase “rotational axis” then refers to therotational axis of the rotational device or the rotational axis of thereference rotational device. When using the test body, the rotationalaxis can be tangential to, or intersect with, the test body or theholder or a test element, or the rotational axis can lie outside of thetest body when the test body is used.

A reflector, as a test element, is aligned in relation to the rotationalaxis in the manner described when the test body is arranged at arotational device or reference rotational device. Or a reflector, as atest element, is alignable in relation to the rotational axis in themanner described when the test body is intended to be arranged at arotational device or reference rotational device. A measurement body, asa test element, is arranged at a distance from the rotational axisand/or in a manner not coaxial with the rotational axis when the testbody is arranged at a rotational device or reference rotational device.Or a measurement body, as a test element, can be arranged in the mannerdescribed in relation to the rotational axis when the test body isintended to be arranged at a rotational device or reference rotationaldevice.

The use of a rotational device and of a reference rotational device in aspecific method will still be discussed in detail below. The test bodyis configured in such a way that it can be attached to part of arotational device or reference rotational device, to be precise in amanner conjointly rotating with this part. The part of the rotationaldevice/reference rotational device can be rotatable about the rotationalaxis relative to a further part of the rotational device/referencerotational device (together with the test body). By way of example, thepart to which the test body can be attached is a rotary plate or arotary table or a rotatable part of a rotary joint or rotary pivotjoint.

The holder of the test body can have an axis of rotational symmetrywhich can be arranged axially flush or substantially axially flush withthe rotational axis of the rotational device or the reference rotationaldevice.

The rotational angle of the test body or of the rotational device ispreferably implemented with the aid of the first test element. Thisrotational angle information can be used to determine the rotationalposition error of the rotational device. The first test element can beattached laterally to the rotational axis and connected directly to theholder. In another variant, the first test element is connectedindirectly to the holder by means of a support or another differentfastening element. Instead of this, or in addition thereto, otherrotational errors, such as e.g. translational errors or furtherrotational errors, as explained in the part relating to the example, canalso be determined by means of the first test element.

The second test element preferably serves to register furthertranslational or rotational deviations, which can occur in addition tothe rotational position error. However, the second test element can alsobe used to determine a rotational position error, as specified in theexemplary embodiments. By way of example, rotational position errors canbe determined by means of the first and the second test element if bothare reflectors, in particular mirrors.

A reflector as a test element can advantageously be used in a method forregistering rotational position errors, as yet to be described below andin the examples, wherein, in the method, a rotational device is coupledto a reference rotational device and the test body is attached to therotational device or the reference rotational device and wherein, in themethod, a rotation of parts of the rotational device and of parts of thereference rotational device is undertaken in such a way that, after therotations, the position of the test body is unchanged, changed only alittle or substantially unchanged, in particular unchanged, changed onlya little or substantially unchanged in relation to an external referencepoint or observation point. In such a method, the one unchanged orminimally changed position of the reflector can be registered by meansof e.g. a sensor, in particular an angle sensor, specifically anautocollimator.

Within the terminology of this invention, a reflector should bedistinguished from a measurement body. The purpose of the reflector isto determine a rotation by a change in direction of reflected radiation,in particular light, after a change in rotational position of thereflector and/or to determine a translation by means of reflectedradiation, e.g. by means of a radiation-based distance sensor.

A measurement body is configured in such a way that the rotation and/ortranslation thereof can be determined by a radiation-less measurement,in particular by means of a coordinate measurement and/or aradiation-less distance measurement.

However, despite distinguishing between the terms reflector andmeasurement body, it is conceivable for a reflector to be able to beused within the aforementioned sense of a measurement body, without thereflective properties for radiation thereof being used. By way ofexample, the surface of a plane mirror before and after a rotation canbe sensed at at least three points using the sensing unit of acoordinate measuring machine, as a result of which the position of thesurface plane before and after the rotation is obtained, and therotation or the rotational angle can be established therefrom.

The term reflector also comprises arbitrarily thin reflection layers,which may be applied to a support body or a surface of a support bodyfor stabilizing purposes. A reflector can e.g. be a mirror, inparticular a plane mirror or a substantially plane mirror, a flat orsubstantially flat mirror or a mirror without curvature or substantiallywithout curvature.

In a further variant, the reflector can be a combination of

-   -   a) a first, partly transparent mirror, preferably a plane mirror        or substantially plane mirror and    -   b) a second, fully reflecting mirror, preferably a plane mirror        or substantially plane mirror,        wherein the partly transparent mirror a) and the fully        reflecting mirror b) are arranged in such a way in relation to        one another that incident radiation is firstly incident on the        first, partly transparent mirror, it partly passes through this        first mirror and is partly reflected thereby, and the radiation        portion passing through the first mirror is subsequently        incident on the fully reflecting mirror b) and        wherein the mirror a) and the mirror b) are arranged at an angle        to one another, preferably at an angle less than 90°.

In another variant, the reflector can be a retroreflector. In a specialvariant, the reflector can be a prism. A light-entry face of the prismcan be partly reflective such that part of the incident light isreflected at this face like it is at a plane mirror and the remainingpart of the light is cast back in an angle-maintaining manner afterreflection at the angled faces of the prism. Preferred variants aredescribed in DE102011012611 (A1). By way of example, a triple prism anda 90 degree prism are described therein, wherein it is possible, inconjunction with an autocollimator, to measure not only the inclinationangle perpendicular to the optical axis but also, simultaneously, theroll angle about the optical axis.

The reflector can also be a combination of a mirror, in particular aplane mirror, a retroreflector and/or a prism.

In a reflector, the rotational angle can be determined, in particular,with an autocollimator or with a distance sensor, as described in theexemplary embodiments, when the test body is rotated in a manner inwhich the reflector is co-rotated. Preferred measuring methods fordetermining the rotational position error are contactless measuringmethods, in particular autocollimation. As a result, no errors aregenerated by sensing forces and the test bodies are spared mechanically.

The following description relates to a mirror, but can apply analogouslyto a retroreflector. A mirror need not be exactly planar and can havewanted non-planar elements on a planar face, for example a prism asmentioned above. Otherwise, possibly present form defects of the mirrorcan be calibrated in a separate step and the error can be taken intoaccount when using the test body.

The phrase “aligned at an angle to the rotational axis” means that thereflector does not point in the direction of the rotational axis orparallel to the rotational axis, but rather in any direction pointingaway from the rotational axis, in the specific case, in a directionorthogonal or substantially orthogonal to the rotational axis. The beamof an autocollimator can be directed onto a reflection face of thereflector and register a change in angle when the mirror is co-rotatedwhen the test body is rotated. Additionally, it is also possible toregister the rotation of the mirror about a further rotational axis,e.g. a rotational axis orthogonal to the rotational axis of the testbody, and to register the rotational deviation in respect of thisfurther rotational axis. Preferably, to this end, the reflector isaligned orthogonally or substantially orthogonally.

In a specific variant of a test body, the first test element is areflector, which is aligned at an angle to the rotational axis andreflects radiation incident thereon in a direction dependent on therotational angle of the test body, and the second test element is areflector, which is aligned at an angle to the rotational axis andreflects radiation incident thereon in a direction dependent on therotational angle of the test body, and the reflectors are arranged at anangle to one another, e.g. arranged orthogonally.

If the first and the second test elements are reflectors, then bothreflectors can be attached together to a common support body, forexample in the form of reflecting coatings. An example of a support bodyis a regular or irregular polyhedron, e.g. a prism, a tetrahedron, ahexahedron, an octahedron, a dodecahedron, an icosahedron.

Specifically preferred examples of support bodies are support bodiesthat have a cross section in the form of a polygon, preferably a regularpolygon. Preferably, a cross section is in the form of an N-gon, whereinN is an integer greater than or equal to 3, preferably a regular N-gon.Examples are three-, four-, five-, six-, seven- or eight-sided crosssections.

More specific examples of a support body are prisms, wherein a prism isunderstood to mean a geometric body which has a polygon as a base area,preferably a regular polygon, and the side edges of which are paralleland of equal length, wherein the side edges extend at an angle to, inparticular in a manner orthogonal to, the base area. A prism with anN-sided base area is preferred, wherein N is an integer greater than orequal to 3, preferably with a regular N-sided base area. Examples are athree-, four-, five-, six-, seven- or eight-sided base area, wherein aregular three-, four-, five-, six-, seven- or eight-sided base area ismost preferable.

Reflectors or reflector layers can be applied to one or more externalfaces of a support body. The support body can be a hollow body withexternal faces. Two or more of the external faces can be provided with areflector or with a reflection layer, wherein, for example, a firstreflection layer on a first face is the first test element and a secondreflection layer on a second face is the second test element. In thecase of a polyhedron, in particular a prism, an end face pointing in thedirection of the rotational axis as one of the external faces can beprovided with a reflector or with a reflection layer.

In one embodiment, the support body has a reflector arrangement whichhas a plurality of reflectors or reflector layers, wherein thereflectors or reflector layers are at an angle to one another and pointin different spatial directions.

When the reflector or the reflector layer is a plane mirror or asubstantially plane mirror, or a planar or substantially planar layer,then the phrase “spatial direction” or “pointing in a spatial direction”refers to the normal vector on the mirror surface, i.e. the normalvectors point in different, e.g. inverted spatial directions, expresseddifferently: in opposite spatial directions.

By way of example, two reflectors or reflector layers can be present ina support body with a reflector arrangement, which reflectors are at anangle of >180° to 360° in relation to one another. The angle between tworeflectors or reflector layers is measured from the reflecting surfaceof one reflector or one reflector layer to the reflecting surface ofanother reflector or another reflector layer. In the case of an angle of360°, the reflectors/reflector layers point in opposite spatialdirections.

By way of example, more than two reflectors or reflector layers can bepresent in a support body with a reflector arrangement, which reflectorsor reflector layers are at an angle in relation to one another and pointin various spatial directions, wherein adjacent reflectors or reflectorlayers are preferably at an angle of >180° to <360° in relation to oneanother, wherein the angle is defined as in the case above. In aspecific preferred variant, neighboring reflectors or reflector layerscan be at an angle ofα=360°−[(N−2)/N]*180°in relation to one another, where N is an integer greater than or equalto 3.

Such a support body and such a reflector arrangement permit so-calledflipping-over measurements in a simple manner without the test bodyhaving to be released from a rotatable part of a rotational device, towhich it is coupled in a conjointly rotating manner, in order to twistthe test body against this part. Measurements according to thisprinciple are described elsewhere in this description and in theexamples. By way of example, the support body can have external faces,which are at the aforementioned angle α in relation to one another,wherein reflectors, in particular plane mirrors, or reflector layers areattached to the external faces. Specific examples of such a support bodyare prisms, as defined and specified above.

In a further possible alternative, in the case of a reflector, thephrase “aligned at an angle to the rotational axis” means that thereflector is aligned in the rotational direction or opposite to therotational direction. In the case of a mirror, the reflection facethereof can be aligned in this manner. The phrase “aligned in therotational direction or opposite to the rotational direction” means thatthe reflector points in the rotational direction or opposite to therotational direction. In the case of a mirror, the reflection facepoints in the rotational direction or opposite to the rotationaldirection. Specifically, a reflection face can be aligned in such a wayin the case of a mirror that a normal vector at a point on thereflection face is tangential to a circle described by the rotationalmovement of the point about the rotational axis. In this embodiment,e.g. a distance sensor, in particular a laser, is used for registeringthe rotational angle, which distance sensor measures a change in thedistance in a rotation of the mirror, from which the rotational anglecan be calculated from trigonometric relationships, as specified in anexemplary embodiment. However, alternatively, use can be made of e.g. anautocollimator in order to measure the rotational angle or a change inrotational position.

A first measurement body, as a first test element, which is arranged ata distance from the rotational axis and/or in a manner not coaxial withthe rotational axis can be any body to which a uniquely definedcoordinate system, which is referred to as workpiece or measurement bodycoordinate system, can be assigned. Examples are a sphere, a cylinder, atriple sphere, a cone, a prism or any other geometric body. Inparticular, the measurement body has one or more reference points, alsoreferred to as “spatial points”, which are determinable with a measuringsystem of the CMM such that the rotational position is determinable bydetermining the position of the reference point or points in differentrotational positions of the measurement body. The reference point orpoints are at a distance from the rotational axis.

The first measurement body can have a marking, e.g. an elevation ordepression in the surface, which can be probed by the tactile measuringhead system of a coordinate measuring machine, in particular by asensing unit as part thereof, such that a spatial point can be uniquelydetermined.

It is also possible to probe a reflector as first test element in orderto determine a change in position. By way of example, in the case of aplane mirror, the surface can be probed at three points and, after achange in the rotational position, probing can once again take place atthree points in order thus to determine the rotational angle in themirror plane.

By way of example, the reference point can be determined by probingusing the tactile measuring system of a CMM. If the test element is asphere, then e.g. the sphere center can be used as reference point, theposition of which can be determined by multiple probing of the spheresurface. By way of example, the rotational device is a rotary table anda test body having a sphere located laterally in relation to therotational axis is positioned on the rotary table. In a first angleposition, the position of the sphere and of the sphere center can beregistered using the measuring system of the CMM, e.g. by way ofsensing. After rotating the rotary table plate and the test body into asecond position, the changed sphere position and the sphere center canbe registered anew and the rotational angle of the rotary table plateand of the test body can be established from the measured values. At thedifferent sphere positions, the sphere center is preferably determinedby multiple probing.

Any measurement body at or in which a reference point or spatial pointis uniquely determinable using the measuring system of the CMM can beused as first measurement body as an alternative to a sphere. Asmentioned above, e.g. the sphere center is the reference point in thecase of a sphere. Possibly present form defects of the measurement bodycan be calibrated in a separate step and the error can be taken intoaccount when the measurement body is used.

As mentioned above, a second one of the test elements can be a secondmeasurement body which is either a rotationally symmetric measurementbody or which has a plurality of faces pointing in different directions.The phrase “second measurement body” serves for distinguishing it fromthe first measurement body. The first measurement body is a specificcase of a first test element and can, as described above, be arranged ata distance from the rotational axis and/or in a manner not coaxial withthe rotational axis.

In particular, one of the test elements, for example the second testelement, can be a rotationally symmetric measurement body, the axis ofsymmetry of which can be arranged in a manner coaxial with therotational axis, i.e. the axis of rotational symmetry thereof can bealigned in a manner coaxial with the rotational axis. Examples of suchrotationally symmetric elements are a sphere, a disk, a ring, such ase.g. a torus, a cylinder, a cone or a combination thereof. A pluralityof spheres arranged in succession along the axis, e.g. a double sphere,can be provided as rotationally symmetric test element. The whole spheresurface is not accessible for the measurement in the case of a sphere ordouble sphere since the test element is connected to the holder at atleast one location.

In a preferred variant, the rotationally symmetric test element is acylinder. Furthermore, a plurality of spheres, in particular a doublesphere, are preferred. In this context, a double sphere, or anarrangement of even more spheres, is considered to be a rotationallysymmetric test element which, like a cylinder, can be measured atdifferent points along the axis of symmetry by means of a sensor. Usinga cylinder or a double sphere, it is possible to determine rotationaldeviations about axes which are orthogonal to the rotational axis of therotational device and the test body attached thereto. Furthermore, it ispossible to determine translational deviations in directions at an angleto the rotational axis. Furthermore, it is possible to determine atranslational deviation in the direction of the rotational axis if adistance measurement is implemented on the upper pole of a sphere, or onthe upper pole of the upper sphere of a double sphere, or on the endface of a cylinder. It is also possible to determine a rotationaldeviation by measuring a plurality of points on the end face of thecylinder, wherein the cylinder should have a sufficient diameter for thepurposes of arranging appropriate sensors, but it can by all means havea low height, i.e. be disk-shaped.

In a second alternative, the second measurement body has a plurality offaces pointing in different directions. In this case, the secondmeasurement body is not rotationally symmetric. Specific examples areprisms, wherein a prism is understood to be a geometric body which has apolygon as a base area and the side edges of which are parallel and ofequal length. Specific examples are a triangular prism, a cuboid, acube, a hexagon, pentagon, octagon and bodies with even more side facespointing in different directions. In such a second measurement body, oneor more distance and/or angle sensors can be directed to one or more ofthe faces. By way of example, a cube can be aligned in such a way that,in relation to a Cartesian coordinate system, two side faces point inthe X and −X direction and two side faces point in the Y and −Ydirection and the remaining two side faces point in the Z and −Zdirection. One or more of these side faces can be assigned distancesensors, by means of which a translation in the corresponding spatialdirection is measurable. The faces can be such that a plurality of angleand/or distance sensors can be assigned at various heights along an X, Yand/or Z-axis of the face such that even a rotation of the measurementbody is registrable. By way of example, the second measurement body canhave rectangular side faces, which enable an arrangement of a pluralityof sensors along the side face. In a further alternative, the secondmeasurement body can be a double cube, which is considered to be ameasurement body in this context. A second measurement body which has anumber of faces pointing in different directions can be advantageouslyused in a method, still described below and in the examples, forregistering rotational position errors, in which a rotational device iscoupled to a reference rotational device and the test body is attachedto the rotational device or the reference rotational device, andwherein, in the method, a rotation of parts of the rotational device andof parts of the reference rotational device is undertaken in such a waythat, after the rotations, the position of the test body is unchanged orsubstantially unchanged. In such a method, a rotational symmetry of thesecond measurement body is not required because the measurement body isnot twisted, or only twisted insubstantially, relative to sensorsassigned thereto.

In one embodiment, the test body has a pedestal connected to the holderor formed on the holder. The pedestal is configured to attach the testbody to a rotational device, in particular to a rotatable part of arotational device. In particular, the pedestal has a larger crosssection at an angle to the rotational axis than the holder. The pedestalpreferably has a metal, metal alloy, ceramic or plastic as a mainmaterial component. The pedestal serves for installation in a CMM or forattaching the test body to a rotational device, such as e.g. a rotarypivot joint or a rotary table, or to a reference rotational device,which will still be described on the basis of a method in which the testbody can be used. The pedestal is configured in such a way that it canbe attached to part of a rotational device or a reference rotationaldevice, preferably in a conjointly rotating manner, i.e. in a manner notrotatable relative to this part. The part of the rotationaldevice/reference rotational device can be rotatable relative to afurther part of the rotational device/reference rotational device. Byway of example, the part to which the pedestal can be attached is arotary plate of a rotary table or a rotatable part of a rotary joint orrotary pivot joint.

In one embodiment, the test body has means for fastening or bearing in acoordinate measuring machine or for fastening or bearing on a rotationaldevice for a coordinate measuring machine, such as a rotary pivot jointor a rotary table. Fastening or bearing on a rotational device means, inparticular, that the test body is fastened or mounted on or below therotational device in the installed position of the rotational device andof the test body.

The means for fastening or bearing are preferably arranged at the holderor at a pedestal, which were described above. Means for fastening orbearing are preferably one or more interlocking connection means or oneor more force-fit connection means.

The test body can be equipped with one or more three-point bearingswhich enable a reproducible assembly in one or more orientations. Usingthis, the test body can be used e.g. for qualifying the variousrotational axes of a rotary pivot joint.

In the case of a three-point bearing, an additional tensile force ispreferably generated between the test body and a part, on or at whichthe test body is mounted, which is also referred to as “pretensioning”.Such a tensile force prevents the test body from jumping out of thebearing. By way of example, depending on the alignment of the test body,jumping out of the bearing can be brought about by the weight thereof orby a movement of the test body.

The pretensioning increases the reproducibility of the orientation ofthe test body. The pretension can be implemented e.g. magnetically,preferably at a central point between a plurality of bearing points, orby the inherent weight of the test body. An additional mass can beattached to the test body in order to increase the mass of the testbody. For the purposes of magnetic pretension, the test body can have amagnet which, for example, can be installed or set into the test body.Such a magnet can exert an attractive force to a ferromagneticsubstrate, for example to a ferromagnetic test object. The pretensioncan also be advantageous if large accelerations occur when qualifyingthe rotational axis, for example as a result of release movements in thecase of latching rotary pivot joints. Further means for pretensioningare screws, hooks, a bayonet or a spring.

Further exemplary means for fastening or bearing are stops, pins,screwed connection means, plug-in connection means, latching connectionmeans or non-slip materials.

An advantage of a three-point bearing lies in high precision. If suchprecision is not necessarily required, the test body can be fastened tothe rotational device using stops, (dowel) pins, screws or other knownfixation means.

In one embodiment, the test body has a reflector which is aligned in thedirection of the rotational axis. In particular, in the direction of therotational axis means that a measurement beam incident parallel to oralong the rotational axis is incident on the reflector in an orthogonalor substantially orthogonal manner. A distance sensor can be aligned(axially) to the reflector in the direction of the rotational axis orparallel thereto and it can register a translational deviation in thedirection of the rotational axis (e.g. in the Z-direction). Variousdistance sensors are usable, such as e.g. optical distance sensors orcapacitive distance sensors, wherein an optical sensor is preferred dueto the mirroring properties of a reflector.

Above, reflectors aligned at an angle to the rotational axis werealready described as first and second test elements. These reflectorscan be combined with a reflector oriented in the direction of therotational axis. There can also be even more reflectors aligned at anangle to the rotational axis. Together, a plurality of reflectors canform an arrangement of reflectors, which is also referred to as areflector array, e.g. in the form of a polyhedron, the sides of whichare formed from the mirrors.

In a preferred variant, the test body has a reflector arrangement whichhas a plurality of reflectors or reflector layers, wherein thereflectors or reflector layers are at an angle in relation to oneanother and point in different spatial directions. As described above,there is no need for a support body in the case of such a reflectorarrangement.

If the reflector or the reflector layer is a plane mirror or asubstantially plane mirror, or a plane or substantially plane layer,then the term “spatial direction” and “pointing into a spatialdirection” relates to the normal vector on the mirror surface, i.e. thenormal vectors point in different, e.g. reverse, spatial directions.

By way of example, two reflectors or reflector layers can be present inthe reflector arrangement, which reflectors or reflector layers are atan angle of >180° to 360° in relation to one another. The angle ismeasured from the reflecting surface of one reflector or one reflectorlayer to the reflecting surface of another reflector or anotherreflector layer. In the case of an angle of 360°, thereflectors/reflector layers point in opposite spatial directions.

By way of example, more than two reflectors or reflector layers can bepresent in the reflector arrangement, which reflectors or reflectorlayers are at an angle in relation to one another and point in variousspatial directions, wherein adjacent reflectors or reflector layers arepreferably at an angle of >180° to <360° in relation to one another. Ina specific preferred variant, neighboring reflectors or reflector layerscan be at an angle ofα=360°−[(N−2)/N]*180°in relation to one another, where N is an integer greater than or equalto 3.

Such a reflector arrangement permits so-called flipping-overmeasurements in a simple manner, without the test body having to bereleased from a rotatable part of a rotational device, to which it iscoupled in a conjointly rotating manner, in order to twist the test bodyagainst this part. Measurements according to this principle aredescribed elsewhere in this description and in the examples.

In a preferred variant, the test body has a plurality of measurementbodies, which are arranged at a distance from the rotational axis and/orin a manner not coaxial with the rotational axis, wherein a notionalline from one measurement body to the rotational axis and a notionalline of an adjacent measurement body to the rotational axis are at anangle of 360°/M with respect to one another, wherein M is an integergreater than or equal to 2, in particular 2-8. In particular, each oneof the measurement bodies has a reference point and a notional line fromthe reference point of a measurement body to the rotational axis and anotional line from the reference point of an adjacent measurement bodyto the rotational axis are at the angle of 360°/M with respect to oneanother. Expressed differently, the reference points preferably form thecorners of a regular N-gon. The reference points can be e.g. spherecenters if the measurement bodies are spheres. Such an arrangement alsopermits in a simple manner the so-called flipping-over measurementswhich are described elsewhere. One of the plurality of measurementbodies which are arranged at a distance from the rotational axis and/orin a manner not coaxial with the rotational axis can be the firstmeasurement body already mentioned above.

If the first and/or the second test elements are reflectors which arealigned at an angle to the rotational axis and if, furthermore, anotherreflector is present, which is aligned in the direction of therotational axis, or if an aforementioned reflector arrangement isformed, which may also contain further reflectors, then all reflectorscan be attached to a common support body, for example in the form ofreflective coatings. Specific examples for support bodies are prisms,wherein a prism is understood to be a geometric body which has a polygonas a base area and the side edges of which are parallel and of equallength, or polyhedrons. The support body can be a hollow body withexternal faces. Specific examples for support bodies are a prism with athree-sided, four-sided, five-sided, six-sided, seven-sided oreight-sided base area, a tetrahedron, a hexahedron, an octahedron, adodecahedron, an icosahedron. Three or more of the (external) faces ofthe support body can be provided with a reflection layer.

In principle, a test element can have one or more further test elements,e.g. a third test element, a fourth test element, etc., in addition tothe aforementioned first and second test elements. Further test elementscan be selected from such elements which were already described as firstor second test element, such as reflectors and test bodies.

If a second one of the test elements is a second reflector aligned oralignable at an angle to the rotational axis, which second reflector isaligned in a different direction to the other reflector if another,first reflector, which is a test element of the test body, is present,then the other direction means, in particular, that both reflectorspoint in the opposite direction or substantially opposite to one anotheror both reflectors are orthogonal or substantially orthogonal to oneanother. Orthogonal to one another means that the reflectors point indirections that are at an angle of 90° to one another. The angle fromthe reflection face of the first reflector to the reflection face of theother reflector then is 360°−90°=270°; the angle between the normals ofthe reflection faces is 90°.

In one variant of the test body, a first one of the test elements is areflector aligned in a manner orthogonal to the rotational axis and asecond one of the test elements is likewise a reflector aligned in amanner orthogonal to the rotational axis, which second one of the testelements is aligned in a different direction to the first reflector,preferably in a manner orthogonal to the first reflector or in theopposite direction to the first reflector, and a further, third testelement is a rotationally symmetric test element, the axis of symmetryof which is arranged in a manner coaxial with the rotational axis,wherein the third test element is preferably arranged at a differentaxial position in relation to the rotational axis than the reflectors.The reflectors are preferably both arranged at the same axial position.This also applies to further embodiments with two reflectors.

In a further variant of the test body, a first one of the test elementsis a reflector aligned in a manner orthogonal to the rotational axis anda second one of the test elements is likewise a reflector aligned in amanner orthogonal to the rotational axis, which second one of the testelements is aligned in a different direction to the first reflector,preferably in a manner orthogonal to the first reflector or in theopposite direction to the first reflector, and a further, third testelement is a reflector aligned in the direction of the rotational axis.

In one embodiment, the test body has a reflector as first and secondtest element. Both reflectors are preferably aligned orthogonal to oneanother, i.e. the reflection faces of the reflectors are at right anglesto one another. By way of example, the first reflector points in theX-direction of a Cartesian coordinate system and the second reflectorpoints in the Y-direction of a Cartesian coordinate system. In thisembodiment, respectively one beam of an autocollimator can be directedto each one of the two reflectors. Firstly, the rotational angle aboutthe rotational axis can be registered separately at both reflectors.Furthermore, a rotational deviation about in each case a further axiscan be registered at each reflector, which further axis is orthogonal inrelation to the rotational axis, as explained in the exemplaryembodiments. It is possible to use two autocollimators and in each casedirect the beam of one autocollimator to one of the reflectors.Secondly, it is also possible to use only one autocollimator and directthe beam by means of a deflection device, preferably an arrangement ofdeflection mirrors, onto both reflectors. In addition to one or moreautocollimators, distance sensors can be directed onto the reflectors,e.g. laser rangefinders, in order to register translational deviations.

If the test body has a reflector as first, second and third testelement, then all three reflectors are preferably aligned in a mannerorthogonal to one another, i.e. the reflection faces of all reflectorsare at right angles to one another. By way of example, the firstreflector points in the X-direction of a Cartesian coordinate system,the second reflector points in the Y-direction of a Cartesian coordinatesystem and the third reflector points in the Z-direction of a Cartesiancoordinate system.

Levers and additional masses can be attached to the test body. Thisrenders it possible to simulate forces and torques occurring during thesubsequent measurement operation. The rotational axis can then bequalified precisely in the manner in which it is also used in practiceduring measurement operation. For a subsequent correction, it is alsopossible to establish the compliance by unloaded and loadedmeasurements. Here, as described in EP0684447 (B1) and DE19518268 (A1),the compliance can encompass a tilt as a result of a torque, a tilt as aresult of a force, a displacement by a torque and/or a displacement by aforce.

Preferably, the test body is movable into its usage position at the testobject and/or removable from the usage position. To this end, thearrangement can have an appropriate movement apparatus and/or anappropriate movement guide. In one embodiment, the test body has acomponent of a linear guide, e.g. a steel roller. In this embodiment, alinear guide, for example a steel roller mounted in a V-profile, isarranged between the test body and the test object. Using this, it ispossible to move the test body out of, or into, the measurement regionof sensors. In alternative embodiments, the test body has a joint oroffset three-point bearings, by means of which the test body can bepivoted or offset out of, or into, the measurement region. If the testbody is displaced, pivoted away or offset, it is possible e.g. toperform work, such as adjustments, on sensors. Offset three-pointbearings are understood to mean that the test body can be brought intoat least two different positions and/or alignments, in whichrespectively an associated three-point bearing is established.

In one embodiment, the test body has one or more actuation devices forsetting the relative position between test body and test object, inorder e.g. to set the coaxial property between test object and a rotarytable. Screw drives are examples of actuation devices.

Alignment elements for aligning the test body can be arranged betweenthe test body and the test object. Examples of alignment elements are atable, such as e.g. an XY-table and/or a tilt table, or a joint, e.g. amonolithic joint, or a flexure bearing, e.g. a bending flexure.

In a further embodiment, the test body has a two-part design. A numberof the above-described test elements, such as mirrors, (double) spheres,cylinders, can be attached to different parts or can be present asindividual parts, which can be assembled in a modular fashion to formthe test body. Thus, test bodies with different components andfunctionalities are producible from different modules. In particular,the holder of the test body has a multi-partite design. By way ofexample, a first test element, e.g. a mirror, is fastened to a lowerpart of the holder and a second test element, e.g. a rotationallysymmetric body, is fastened to an upper part. A three-point bearing canbe situated between the two parts.

In a further variant of the invention, the test body has a face, which,from the perspective of the assembly position at a rotational device, ismovable against a sensing unit, sensor or measuring head of a CMM.During the movement, the rotational device is moved together with thetest body and, in the process, the face is moved against the sensingunit, sensor or measuring head. In relation to the movement against asensing unit, this method is referred to as “probing with the testbody”. By multiple repetition of this sensing movement, thereproducibility of the movement of the rotational device, for examplealong a linear guide, can be tested. Alternatively, the test body canalso contain a sensing unit.

In a further aspect, the invention relates to an arrangement,comprising:

-   -   a rotational device,    -   a test body which is arranged or fastened to the rotational        device,    -   a plurality of sensors, which are respectively assigned to one        or more of the test elements of the test body and configured to        measure deviations in respect of at least one of the degrees of        freedom of movement.

Rotational errors can be established from the deviations of the realrotational movement from the ideal or desired rotational movement inrespect of degrees of freedom of movement, i.e. translational androtational degrees of freedom.

The sensor is configured to generate a measurement signal correspondingto a position of the test element during operation of the arrangement.

By way of example, the sensor can be a magnetoresistive sensor, a Hallsensor, which operates in accordance with the electromagnetic Halleffect, an optical sensor, a sensor operating in accordance with thepiezo-resistive effect, a capacitive sensor, an eddy current sensorwhich is configured for measuring the distance and/or relative position,or a sensor which operates in accordance with at least one of theaforementioned functionalities and/or at least one functionality thathas not been mentioned. A number of magnetoresistive sensors and Hallsensors in particular can also be arranged on a common support, e.g. amicro-support that is similar to a microchip. Each one of the sensors onthe common support then, in particular, registers a different degree offreedom of the movement. By way of example, all degrees of freedom ofthe movement can be registered with two such supports which each carrythree sensors for registering three linearly independent degrees offreedom and which are arranged at different axial positions. Thedirection of a magnetic field prevalent at the location of the supportcan also be measured by the plurality of sensors on a support. Opticalsensors register e.g. one of a plurality of markings formed on the testelement when the marking moves past from the view of the sensor. In adifferent type of optical sensor, e.g. a laser triangulation and/or acomparison with a comparison light beam which is not influenced by thetest element is performed, like in the case of an interferometer.Patterns projected onto the test element are registered in a furthertype of optical sensor.

In particular, the test element is configured in accordance with themeasurement principle of the sensor. By way of example, the test elementcan have a permanent magnetic material in order to be able to measure inaccordance with the Hall effect or the magnetoresistive measurementprinciple. Alternatively or additionally, the test element (e.g. acylinder or a spherical test element) can have an electricallyconductive surface for a capacitive or inductive sensor and/or amirroring surface for reflecting measurement radiation for an opticalsensor. A mirroring or partly reflecting surface can be formed e.g. on acylinder-shaped, cone-shaped or torus-shaped test element. In any case,the sensor generates a measurement signal which contains informationabout the position of the test element. If the test element has areflector which reflects incident measurement radiation as a function ofthe alignment of the reflector, it is possible to determine therotational position.

A calibration of the sensor arrangement formed by the test element andthe sensor may be necessary in order to be able to establish theposition of the test element when the arrangement is in operation.Therefore, it is preferable to calibrate the arrangement for measuringcoordinates of a workpiece in respect of determining the position of thetest element, i.e. measurement signals of the sensor are to be assignedthe corresponding values of the position or relative position. Here, forexample, comparison measurements are performed and/or use is made ofcalibration standards that are known exactly in respect of thedimensions and form thereof and in respect of position relative to thearrangement.

A plurality of sensors together can use at least one test element forsignal generation purposes. However, it is also possible that a separatetest element is assigned to each one of a plurality of sensors.Furthermore, it is possible that a sensor component has more than onesensor.

A rotational device has a rotational movability of a first part and asecond part about at least one rotational axis, wherein the first partand the second part have rotational movability relative to one anotherdue to the rotational movability of the rotational device and whereinthe first or the second part is configured to hold either the workpieceor a coordinate measuring apparatus, e.g. the sensing unit or sensinghead, in order to enable a rotation of the workpiece or the coordinatemeasuring apparatus. The invention therefore also relates to rotationaldevices which have rotational movabilities about two rotational axes(e.g. a so-called rotary pivot joint with two rotational axes extendingat an angle to one another) or about more than two rotational axes.

In one embodiment, the first or the second part of the rotational deviceis embodied to hold a workpiece. In the present arrangement, a test bodyaccording to the invention is arranged on, and/or fastened to, the firstor the second part instead of a workpiece for the purposes of qualifyingthe axis. The other part is, in particular, configured to be fastened toa base of a coordinate measuring machine (CMM) and/or to be positionedon a base such that this part is immovable relative to the base and thetest body, with the other part, can be rotated relative to the base. Byway of example, the first and second parts can be parts of a rotarytable, on or at which the test body is arranged or fastened in order tobe able to be brought in various rotational positions and in order toperform an establishment of the rotational errors in the variousrotational positions.

In accordance with a further embodiment of the arrangement, the first orthe second part of the rotational device is configured to hold acoordinate measuring apparatus. In this case, the first and the secondpart enable a rotation of the coordinate measuring apparatus by means ofa relative movement. By way of example, so-called rotary pivot joints,which enable a rotational movability in respect of two rotational axesextending at an angle and, in particular, orthogonal to one another, areknown. However, rotational devices which merely enable a rotationalmovability in respect of a single rotational axis or rotations aboutmore than two rotational axes are also known.

In one variant, and arrangement is provided, wherein

-   -   the first and/or the second test element of the test body is a        reflector,    -   one or more angle sensors, preferably optical angle sensors, are        assigned to the reflector or reflectors,        wherein the optical angle sensor or sensors is/are configured to        register a rotation of the test body about a rotational axis of        the rotational device and/or a rotation of the test body about        one or more axes at an angle to the rotational axis and/or an        unchanging position of the test body. The angle sensor registers        a rotation of the reflector which co-rotates with the test body        because it is rigidly connected to the test body. Therefore, it        is also possible to establish the rotation of the test body by        measuring the rotation of the reflector.

Examples for sensors or of devices which can be used as angle sensorsfor the purposes of this invention are optical angle sensors, such asautocollimators, laser rangefinders, laser interferometers, capacitivesensors, including capacitive distance sensors for the purposes of anangle measurement, magnetoresistive sensors, such as magnetoresistiveangle sensors or magnetoresistive distance sensors which are used forthe purposes of the angle measurement.

In a further variant, one or more distance sensors are assigned to oneor more reflectors of a test body. By way of example, distance sensorscan be capacitive sensors, eddy current sensors, magnetic field sensors,optical distance sensors, such as lasers, interferometers, or mechanicalinductive sensing units, wherein optical distance sensors are preferredin the case of a reflector.

By way of example, an autocollimator and/or an optical sensor, inparticular a laser interferometer or laser rangefinder, can be assignedto a reflector. One or more distance sensors can be assigned to arotationally symmetric test element. A plurality of sensors, or some ofthe plurality of sensors, are preferably configured or arranged in sucha way that these can be used to measure distances in different spatialdirections and/or angles about different rotational axes such thatdeviations can be measured in respect of a plurality of translationaland rotational degrees of freedom of movement. Which deviations can beestablished with which test body, in particular when using reflectors,and with which arrangement of sensors is explained, in particular, inexemplary embodiments of the description of the figures. An opticalangle sensor directed to a reflector, in particular an autocollimator,can for example register a rotation of the reflector about axes whichare at an angle to the spatial connection axis between sensor andreflector. By way of example, if a measurement beam of an autocollimatoris incident on the mirror in the X-direction, then it is possible toregister a rotation of the mirror about the Y-axis and the Z-axis and itis possible to determine the rotational angle. By way of example, if ameasurement beam of an autocollimator is incident on the mirror in theY-direction, then it is possible to register a rotation of the mirrorabout the X-axis and the Z-axis and it is possible to determine therotational angle.

In a further variant, an arrangement is made available, wherein

-   -   the first test element of the test body is a measurement body,        as already described, which is arranged at a distance from the        rotational axis and/or in a manner not coaxial with the        rotational axis,    -   one or more sensors, in particular an optical sensor or a        tactile measuring head system of a coordinate measuring machine,        are assigned to the measurement body,        wherein the sensor or sensors, in particular the measuring        system, is/are configured to register a rotation of the test        body about a rotational axis of the rotational device and/or a        rotation of the test body about one or more axes at an angle to        the rotational axis and/or an unchanging position of the test        body.

The measuring system of a coordinate measuring machine, e.g. an opticalmeasuring system or a tactile sensing measuring system, can be part ofthe arrangement if the rotational device and the test body are set up ina coordinate measuring machine, i.e. if the arrangement is establishedin a coordinate measuring machine. Within this meaning, the measuringsystem of the coordinate measuring machine, in particular an opticalsensor or a tactile measuring head system, is considered to be anassigned sensor within the meaning of this arrangement. Naturally, anoptical sensor or a tactile measuring head system is only assigned tothe measuring head for the purposes of establishing rotational errorsand only for as long as the arrangement is established in the coordinatemeasuring machine.

In a preferred arrangement, the test body is arranged or fastened by wayof the holder on the rotational device, for example by way of anabove-described bearing, in particular a three-point bearing. Forarranging or fastening purposes, use can be made of a holding elementwhich is arranged between the test body and the rotational device andwhich will still be described below and in the exemplary embodiments.

In a further aspect, the invention relates to a method for establishingrotational errors, also referred to as movement errors, of a rotationaldevice for a coordinate measuring machine in respect of a plurality ofdegrees of freedom of movement, in which a real rotational movement ofthe rotational device differs from an ideal rotational movement, themethod comprising the following steps:

-   -   a) rotating a test body, as described above, which is arranged        at, or fastened to, the rotational device, about a rotational        axis,    -   b) Establishing rotational errors by means of a plurality of        sensors, which are respectively assigned to one of the test        elements of the test body and configured to measure deviations        in respect of at least one of the degrees of freedom of        movement.

The method can be performed using an above-described arrangement. Asdescribed above, the test body has a holder which is rotatable about arotational axis and configured to fasten the test body in respect of arotational axis about which the test body is to be rotated forestablishing the rotational errors. In the method, the rotational axisis the rotational axis of the rotational device or the rotational axisabout which parts of the rotational device are rotatable in relation toone another.

The information obtained by the method can be taken into account whenusing the rotational device, in particular in the subsequent measurementoperation. One option for taking this into consideration lies in thecomputational correction of the movement, in particular by means of amathematical model.

In the method, a test body which has an axial extent in the direction ofthe rotational axis of the rotational device is used in a preferredembodiment. In particular, use is made of a test body which has, as atest element, a double sphere, a cylinder or an elongate prism which canhave any cross section (quadratic, rectangular, hexagonal etc.). One ormore sensors, preferably at least two sensors, which measure therelative position of the sensor and the test element in different,preferably mutually orthogonal spatial directions, are assigned to eachtest element, wherein the directions can be e.g. aligned orthogonally tothe rotational axis.

By way of example, the measurement of various axial positions renders itpossible to measure wobble errors due to a deviation of the alignment ofrotatable and/or rotationally symmetric parts of the rotational device.A wobble error is a rotational movement error and can be described as arotation about one or more spatial axes that are orthogonal to therotational axis of a rotational device. By way of example, if therotational axis of a rotor of a rotational device lies in theZ-direction, a wobble error can be described by an additional, unwantedrotation of the rotor about the X-axis and/or Y-axis, wherein thisrotation about the X-axis and/or Y-axis occurs during the rotation ofthe rotor about the Z-axis and the rotor can rotate a number of timesand in different rotational directions about the X-axis and/or Y-axisduring the rotation. In the case of additional deviations from the idealrotational movement, additional movements can be superposed on thewobble movement. Naturally, further errors can occur in addition to awobble error such that the axis of symmetry can, in practice, alsoperform different movements. By way of example, a radial run-out can beadded to the wobble error such that an elliptic or circular movementthat is not concentric with the rotational axis is superposed on thewobble error. A radial run-out can also be the result of a wobblemovement.

Preferably, at least one sensor/test element pair (in this case, e.g.the same measurement body can interact with a different sensor) isadditionally provided, which pair is configured to measure changes inthe axial position between test element and sensor. If two suchadditional sensor element/test element pairs are arranged at differentaxial positions, it is consequently possible to register thecorresponding two degrees of freedom of movement and e.g. the wobbleerror or other errors can be determined from the totality of availableinformation. Here, there is no need for a separate measurement body tobe available for each one of the pairs. Rather, the same measurementbody can be used by e.g. two sensors, a plurality of sensors or allsensors.

In one embodiment of the method, the test body has a reflector as firstand/or second test element and one or more sensors, preferably anglesensors, most preferably optical angle sensors, are assigned to thereflector or reflectors, comprising one or more of the following steps:

-   -   registering a rotation of the test body about a rotational axis        of the rotational device by means of the sensor/sensors and/or    -   registering a rotation of the test body about one or more axes        at an angle to the rotational axis by means of the        sensor/sensors.

In respect of this method embodiment, reference is made to thearrangement in which the first and/or the second test element of thetest body is a reflector and one or more sensors, in particular opticalangle sensors, are assigned to the reflector or reflectors, and to theexplanations made there. As already specified above, an optical anglesensor, in particular an autocollimator, directed to a reflector canregister e.g. a rotation of the reflector about axes which are at anangle to the spatial connection axis between sensor and reflector. Byway of example, if a measurement beam of an autocollimator is incidenton the mirror in the X-direction, then it is possible to register arotation of the mirror about the Y-axis and Z-axis and the rotationalangle can be determined. It is possible to measure a rotation of theabout the Y-axis and the Z-axis by means of an autocollimator and aretroreflector in the form of a prism and additionally to measure arotation about the X-axis (roll angle), i.e. the rotation about theoptical axis. To this end, use can be made of a measuring system asdescribed in DE102011012611 (A1).

By way of example, if a measurement beam of an autocollimator isincident on the mirror in the Y-direction, then it is possible toregister a rotation of the mirror about the X-axis and the Z-axis andthe rotational angle can be determined. In an analogous manner it isalso possible to measure the rotation about the Y-axis (roll angle)using a specific measuring system made of an autocollimator and aretroreflector in the form of a prism, as is described in DE102011012611(A1).

In one variant of the embodiment described above, one or more—preferablyoptical—distance sensors are assigned to the reflector or reflectors,and the method comprises: establishing one or more translation errors bymeasuring the distance between the reflector/the reflectors and theassociated sensor/sensors.

By way of example, if a reflector points in the X-direction, it ispossible to measure a translation of the test body in the X-directionusing an optical distance sensor by way of example, the measurement beamof which is directed in the X-direction onto the reflector. Thecorresponding principle applies to other spatial directions in aCartesian coordinate system.

In a further aspect, the invention relates to a specific method forestablishing the rotational position error of a rotational device. Inthis method, use can be made of the test body described above. Arotational position measuring system of the rotational device can becalibrated using the method. Moreover, the established rotationalposition error can be converted into a correction model by acomputational model of the rotational device.

In the method for establishing the rotational position error, arotational device, which has two parts rotatable relative to oneanother, is coupled to a reference rotational device, which likewise hastwo parts rotational relative to one another, wherein one of the partsof the rotational device is coupled to one of the parts of the referencerotational device in a conjointly rotating manner and the other part ofthe rotational device is rotatable relative to the other part of thereference rotational device, and an above-described test body isattached to the rotational device or to the reference rotational device,and the method comprises the following steps:

-   -   establishing a first rotational position of the test body using        the sensor/sensors, in particular angle sensors,    -   rotating the two parts of the reference rotational device        relative to one another and rotating the two parts of the        rotational device relative to one another in such a way that the        test body is rotated into a second rotational position which        corresponds, or substantially corresponds, to the first        rotational position,    -   establishing a second rotational position of the test body using        the sensor/sensors, in particular angle sensors.

The rotating of the two parts of the reference rotational devicerelative to one another and rotating of the two parts of the rotationaldevice relative to one another is preferably implemented in oppositedirections such that a rotation of the two parts of the referencerotational device is compensated for by a counter rotation of the twoparts of the rotational device. This method will be described in moredetail below.

The correction values determined using the test body according to theinvention and the method described above can also be used for thepre-correction of an online-corrected rotary table. An example of anonline-corrected rotary table is described in the patent applicationPCT/EP2011/061681. Reproducible errors may be generated in theonline-corrected rotary tables as a result of systematic errors of ameasuring scale element (e.g. double sphere integrated into the rotarytable) described in PCT/EP2011/061681 and assigned sensors (e.g.distance sensors, which measure distances to the spheres). By means ofthe measurement using a test body and a method in accordance with thepresent invention, these systematic errors can be established andoptionally corrected at the later stage. When the method of the presentinvention is performed, the online correction from PCT/EP2011/061681 canbe activated or deactivated.

If the online correction from PCT/EP2011/061681 is kept active duringthe measurement in accordance with the present method, the error of theonline correction system is obtained directly. If the online correctionis deactivated during the measurement in accordance with the presentmethod, correction values from the online correction and correctionvalues from the present method are obtained and can be compared to oneanother. The comparison provides the error of the online correctionsystem, i.e. a deviation between a correction value of the onlinecorrection system and a corresponding correction value which wasestablished according to the present method corresponds to the error ofthe online correction system.

Furthermore, the scope of the invention includes a computer programwhich executes and/or controls the steps of the method according to theinvention. In particular, the computer program has program code meanswhich may be stored on a computer-readable data medium.

Moreover, the scope of the invention includes a data medium, on which adata structure is stored which, after being loaded into a core and/ormain memory of a computer or computer network, executes and/or controlsthe steps of the method according to the invention.

Under II, the following subject combinations are also disclosed, whereinthe specified reference signs establish a reference to the figures inmerely an exemplary manner for explanation purposes.

-   1. A test body (1; 100; 101; 102; 103; 104; 105) for establishing    one or more rotational errors of a rotational device (2; 201), in    particular of a rotational device for a coordinate measuring    machine, in respect of one or more degrees of freedom of movement,    in which a real rotational movement of the rotational device (2;    201) differs from an ideal rotational movement, wherein the test    body comprises:    -   a holder (3, 300), which is rotatable together with part of the        rotational device (2, 201) about a rotational axis (D; A; B) and        which is embodied to arrange or fasten the test body in relation        to the rotational axis about which the test body is to be        rotated for establishing the rotational error or errors,    -   a plurality of test elements (5, 8, 9; 5, 10; 500, 501, 800;        500, 502, 800; 800, 900, 1000; 503) rigidly connected to the        holder or formed on the holder, wherein each one of the test        elements serves to establish the rotational error in respect of        one or more of the degrees of freedom of movement,    -   wherein a first one of the test elements is a reflector (5; 500;        503) which is aligned at an angle to the rotational axis and        reflects radiation incident thereon in a direction dependent on        the rotational angle of the test body, or    -   wherein a first one of the test elements is a first measurement        body (1000) which is arranged at a distance from the rotational        axis and/or in a manner not coaxial with the rotational axis        such that the rotational angle of the test body is determinable        by an associated sensor or by the measuring system of a        coordinate measuring machine on the basis of the rotational        position of the test element,    -   wherein a second one of the test elements is a reflector (501)        which is aligned at an angle to the rotational axis and reflects        radiation incident thereon in a direction dependent on the        rotational angle of the test body and which, if another        reflector (500) which is a test element of the test body is        present, is aligned in a different direction to the other        reflector (500) and which, if another reflector which is a first        test element of the test body is present, can be attached        together with the other reflector at a common support body, or    -   wherein a second one of the test elements is a reflector (502)        which is aligned in the direction of the rotational axis and        which, if another reflector (500) which is a first test element        of the test body is present, can be attached together with the        other reflector (500) at a common support body, or    -   wherein a second one of the test elements is a second        measurement body (8, 9; 10; 800; 800, 900) which is either a        rotationally symmetric measurement body (8, 9; 10; 800; 800,        900) or which has a face pointing in one direction or a        plurality of faces pointing in different directions.-   2. The test body as claimed in point 1, comprising a pedestal (4;    400) connected to the holder (3; 300) or formed on the holder (3;    300), wherein the pedestal is configured to attach the test body to    a rotational device.-   3. The test body as claimed in one of the preceding points,    comprising means for fastening or bearing in or on a coordinate    measuring machine or for fastening or bearing on a rotational device    for a coordinate measuring machine.-   4. The test body (104) as claimed in one of the preceding points,    wherein the first test element is a measurement body (1000) which    has one or more reference points (P) determinable with a measuring    system of the coordinate measuring machine such that the rotational    angle of the test body (104) is determinable by determining the    position of the reference point or points (P) in various rotational    positions of the measurement body (1000).-   5. The test body as claimed in one of the preceding points,    -   wherein the first test element is a reflector aligned at an        angle to the rotational axis, the second test element is a        reflector aligned at an angle to the rotational axis and there        is at least one further reflector as a further test element,        which is likewise aligned at an angle to the rotational axis,        and wherein the reflectors are attached to the outer faces of a        common polyhedron-shaped support body.-   6. The test body (100) as claimed in one of the preceding points, in    which the first test element is a reflector (500) which is aligned    at an angle to the rotational axis and reflects radiation incident    thereon in a direction dependent on the rotational angle of the test    body, and    -   the second test element is a reflector (501) which is aligned at        an angle to the rotational axis and reflects radiation incident        thereon in a direction dependent on the rotational angle of the        test body, and    -   wherein a third one of the test elements is a rotationally        symmetric test element (800), the axis of symmetry of which is        arranged in a manner coaxial with the rotational axis.-   7. The test body (102) as claimed in one of the preceding points,    comprising, as a third test element, a reflector which is aligned in    the direction of the rotational axis if the second test element is    not a reflector aligned in the direction of the rotational axis.-   8. An arrangement comprising:    -   a rotational device (2; 201),    -   a test body (1) as claimed in one of points 1-7, which is        arranged or fastened to the rotational device (2; 201),    -   a plurality of sensors (73, 74, 75, 76, 77, 88; 81, 88, 741,        761; 79) which are respectively assigned to one or more of the        test elements of the test body (5, 8, 9; 500, 501; 503) and        configured to measure deviations in respect of at least one of        the degrees of freedom of movement.-   9. The arrangement as claimed in point 8, wherein    -   the first and/or the second test element of the test body is a        reflector (5),    -   one or more angle sensors (88) are assigned to the reflector or        reflectors,    -   wherein the optical angle sensor or sensors is/are configured to        register a rotation of the test body (1) about a rotational axis        (D; B) of the rotational device (2; 201) and/or a rotation of        the test body (1) about one or more axes at an angle to the        rotational axis (D, A, B) and/or an unchanging position of the        test body (1).-   10. The arrangement as claimed in point 9, wherein the angle sensor    is an autocollimator, a laser interferometer or a magnetoresistive    angle sensor.-   11. The arrangement as claimed in point 9 or 10, wherein one or more    distance sensors (741, 761) are assigned to the reflector or    reflectors.-   12. The arrangement as claimed in point 8, wherein    -   the first test element of the test body is a measurement body        (1000) which is arranged at a distance from the rotational axis        and/or in a manner not coaxial with the rotational axis,    -   one or more sensors, in particular an optical sensor or a        tactile measuring head system of a coordinate measuring machine,        are assigned to the measurement body (1000),    -   wherein the sensor or sensors, in particular the measuring        system, is/are configured to register a rotation of the test        body about a rotational axis of the rotational device and/or a        rotation of the test body about one or more axes at an angle to        the rotational axis and/or an unchanging position of the test        body.-   13. A method for establishing rotational errors of a rotational    device (2; 201) for a coordinate measuring machine in respect of a    plurality of degrees of freedom of movement, in which a real    rotational movement of the rotational device (2; 201) differs from    an ideal rotational movement, the method comprising the following    steps:    -   a) rotating a test body (1; 100; 101; 102; 103; 104; 105) as        claimed in one of points 1-8, which is arranged at, or fastened        to, the rotational device (2; 201), about a rotational axis (D;        A; B),    -   b) establishing rotational errors by means of a plurality of        sensors (73, 74, 75, 76, 77, 88; 81, 88, 741, 761; 79), which        are respectively assigned to one of the test elements (5, 8, 9;        500, 501; 503) of the test body and configured to measure        deviations in respect of at least one of the degrees of freedom        of movement.-   14. The method as claimed in point 13, wherein an angle measuring    system of the rotational device is calibrated using the established    rotational errors.-   15. The method as claimed in point 13 or 14, wherein the test body    has a reflector (5) as first and/or second test element and one or    more angle sensors (88) are assigned to the reflector or reflectors,    the method comprising one or more of the following steps:    -   registering a rotation of the test body (1) about a rotational        axis (D; B) of the rotational device (2; 201) by means of the        angle sensor/sensors and/or    -   registering a rotation of the test body (1) about one or more        axes at an angle to the rotational axis (D, B) by means of the        angle sensor/sensors.-   16. The method as claimed in point 15, wherein one or more distance    sensors (741, 761) are assigned to the reflector or reflectors (5),    the method comprising the following step:    -   establishing one or more translation errors by measuring the        distance between the reflector/reflectors and the assigned        distance sensor/sensors.        III. Holding Element

A holding element disclosed below can be used, for example, in themethod described under I and in an arrangement for performing themethod. It can also be used in a common arrangement with the test bodydescribed under II. The holding element enables an alignment of arotational device for establishing movement errors.

What is specified is a holding element for holding a rotational device,which has a part rotatable in relation to a rotational axis, or whichhas a plurality of parts rotatable about rotational axes, or for holdinga sensor arrangement, which has a plurality of sensors, wherein thesensors are configured to measure deviations in respect of at least oneof the degrees of freedom of movement of the rotational device,

wherein the holding element comprises:

-   -   a first holder for holding the rotational device or sensor        arrangement,    -   a support, to which the first holder is fastened, wherein the        support has at least a first coupling region and a second        coupling region, by means of which the holding element is        coupleable to a base, and        wherein the first coupling region is configured to couple the        holding element in a first position and/or orientation to the        base such that the sensor arrangement or rotational device held        by the holding element is arranged in a first position and/or        orientation when coupling the first coupling region to the base,        and        wherein the second coupling region is configured to couple the        holding element in a second position and/or orientation to the        base such that the sensor arrangement or rotational device held        by the holding element is arranged in a second position and/or        orientation when coupling the second coupling region to the        base.

The position and/or orientation of the holding element, or else otherpositions and orientations specified in this description, are preferablyreproducible. Instead of the term “orientation”, the synonymous term“alignment” can be and is used as well.

In the case of a rotational device with a plurality of parts rotatableabout rotational axes, the rotational axes are preferably not coaxial toone another.

According to a basic concept, the holding element is an intermediateelement, by means of which the rotational device or sensor arrangementcan be arranged in a preferably reproducible location on a base. Insteadof arranging and aligning the rotational device directly on the base,the holding element, to which the rotational device or the sensorarrangement is fastened, is arranged on the base. As a result of theembodiment thereof, the holding element enables a pluralityof—preferably reproducible—locations on the base, depending on how it isoriented relative to the base, in particular depending on the side withwhich it is placed onto the base or coupled to the base. Whenreorienting the holding element, the rotational device or the sensorarrangement is likewise reoriented—preferably in a reproduciblemanner—since there is a secure connection between the holding elementand the rotational device or the sensor arrangement.

As a result of the embodiment of the coupling regions of the holdingelement it is possible to couple the holding element with a preferablyreproducible orientation and preferably also in a reproducible positionon the base. Accordingly, the rotational device or the or sensorarrangement can also be oriented with a reproducible orientation andpreferably also in a reproducible position relative to the holder andhence also relative to the base.

In particular, the following advantages arise as a result of the holdingelement:

-   -   The equipping times are minimized. It is possible to switch        quickly between the measurement/qualification of two different        axes without needing to disassemble the rotational device.    -   It is possible to use a plurality of holding elements for        testing a plurality of rotational devices. By way of example,        one of the rotational devices can be measured in one holding        element, while another rotational device is prepared in a        further holding element.    -   The coupling regions ensure an unchanging spatial orientation of        the rotational device.    -   The coupling regions ensure an unchanging position and/or        orientation of the rotational device.    -   The rotational device can be tested in the subsequent installed        position which is used when measurements are taken with the        rotational device.    -   The holding element can be used for determining the compliance        of a rotary pivot joint in different installed positions, also        in combination with adapted test bodies.    -   Using the holding element, in particular using an angular        support which is yet to be described below, it is possible to        qualify a one-stage rotational device, e.g. a rotary table, in        different installation positions, such as horizontal and        vertical.    -   A sensor arrangement can be oriented in such a way that a        rotational device, to which a test body has been attached (e.g.        a test body which has a double sphere standard), can be        qualified in the installed position thereof. In this variant,        the rotational device is installed e.g. in a coordinate        measuring machine for a subsequent measurement and a test body        is attached to one of the axes. The sensor arrangement can be        oriented toward the test body in a fitting manner by way of the        holding element.

Specifically, the first orientation, in which the rotational device isarranged, corresponds to a predetermined orientation of a firstrotational axis of the rotational device and the second orientation, inwhich the rotational device is arranged, corresponds to a predeterminedorientation of a second rotational axis of the rotational device suchthat, when the first coupling region is coupled to the base and when thesecond coupling region is coupled to the base, respectively onerotational axis of the rotational device is aligned in the predeterminedorientation thereof. In principle, a predetermined orientation can beany orientation which is required or desired for performing ameasurement with or on the rotational axis. The predeterminedorientation of the first rotational axis of the rotational device andthe predetermined orientation of the second rotational axis of therotational device can be the same relative to an external reference.Elsewhere in this description, a method is presented where a rotationalaxis of a rotational device is brought into a specific orientationrelative to the rotational axis of a reference rotational device suchthat the relevant axis of the rotational device and the axis of thereference rotational device are coaxial or substantially coaxial withone another. Using the method, it is possible to determine movementerrors of the rotational device, in particular rotational positionerrors. If the base is part of a further rotational device, inparticular of a rotary table, as is still described below, then thefirst orientation therefore can be such that the first rotational axisis concentric or coaxial, i.e. flush, with the rotational axis of therotary table. Accordingly, the second orientation can be such that thesecond rotational axis is concentric or coaxial, i.e. flush, with therotational axis of the rotary table after a corresponding reorientationor realignment of the holding element and the rotational deviceconnected therewith.

In a further, alternative or complementary variant, the predeterminedorientation of a rotational axis of the rotational device is a rotationin relation to an externally fixed sensor arrangement. By way of examplea test body can be attached to a part of the rotational device rotatableabout a first rotational axis, which test body e.g. has a double spherestandard. The test body, which is attached to the holding elementtogether with the rotational device, is oriented toward the sensorarrangement in an ideal manner with the aid of the holding element andmovement errors of the first rotational axis can be established. Ifmovement errors of the second rotational axis are intended to beestablished, the test body can be attached to a part of the rotationaldevice rotatable about the second rotational axis, and the test body andthe rotational device can be reoriented with the aid of the holdingelement until, once again, an ideal orientation of the test body inrelation to the sensor arrangement is established.

By way of example, the rotational device is a rotary table, a rotaryjoint with a rotational axis or a rotary pivot joint with two or morerotational axes.

By way of example, the sensor arrangement has sensors which are orientedin different spatial directions. Furthermore, the sensor arrangement canhave a sensor holder. Preferred sensors are distance sensors, which arealso specified elsewhere in this description and which measure thedistance to a test element described elsewhere in this description,wherein the test element can be part of a test body which is likewisedescribed elsewhere and which can be attached to a rotational devicewith a rotational axis to be qualified.

In particular, the invention relates to rotational devices which areusable in coordinate measuring machines (abbreviated to CMM below),machine tools, robots and other applications in which a high accuracy isdecisive. The parts of the rotational device rotatable in relation toone another are also rotatable relative to one another after therotational device is fastened to the holding element. By way of example,one of the parts is fastened to the holding element, or held by theholding element, while other parts are movable relative to this part.

The base can be any substrate on which the rotational device is intendedto be positioned for qualifying a rotational axis.

The surface of the base, on which the holding element is placed andcoupled, is also referred to as “clamping face”.

In particular, the base is a rotatable part of a further rotationaldevice, in particular of a rotary table or of a further rotary (pivot)joint.

Specifically, the base is the rotary plate of a rotary table. In afurther specific variant, the rotary table is a so-called referencerotary table, the rotational position or change in rotational positionof which is known accurately. If the rotational device is positioned ona reference rotary table by means of the holding element, a specificmethod for establishing rotational errors, in particular the rotationalposition error of the rotational device, can be performed, which willstill be explained below and in the exemplary embodiments.

The holding element has a support which is a central supporting part ofthe holding element. The support has the coupling regions alreadymentioned above. The support has one or more holders, to which arotational device can be attached. By way of example, if a two-stagerotational device (rotational device with two rotational axes) isintended to be tested in different installation positions, e.g.horizontal and vertical, a second holder, which is arranged in relationto the first holder in accordance with the desired installationposition, is advantageous.

The support is configured in such a way that the holding element can bepositioned at or on the base in at least two—preferablyreproducible—orientations.

In a specific embodiment, the support has a first limb and a secondlimb, which are at an angle to one another, wherein a holder is fastenedto one of the limbs, preferably at the inner side of the limb, andwherein the first limb has the first coupling region, preferably at theouter side thereof, and the second limb has the second coupling region,preferably at the outer side thereof. Such an angle support isadvantageous for two-stage and multi-stage rotary pivot joints. Theangle between the limbs is preferably equal, or substantially equal, tothe angle between two rotational axes of a rotational device to bequalified; by way of example, the angle is 90° in the case of a rotarypivot joint with rotational axes that are at a 90° angle in relation toone another. The angle support is preferably made of solid material witha relatively high density, in particular metal, preferably steel. Asolid and high-mass embodiment is advantageous for reducing deformationsof the support, for example by possible probing forces during thequalification. However, to the extent that deformations of the supportoccur, correction by calculation is also possible if weights andtorques, or probing forces and lever lengths are known. Furthermore, asolid and high-mass embodiment of the support is advantageous for stablepositioning and storage on a base.

In principle, the support can also have further coupling regions inaddition to a first and a second coupling region. In one embodiment, thesupport has a third coupling region, by means of which the holdingelement is coupleable to the base, wherein the third coupling region isconfigured to couple the holding element in a third position and/ororientation to the base such that the sensor arrangement or rotationaldevice held by the holding element is arranged in a third positionand/or orientation when coupling the third coupling region to the base.This principle can be continued for further coupling regions (fourth,fifth, etc.).

A third coupling region is advantageous if a rotary pivot joint withthree rotational axes is intended to be qualified. In one embodiment,the support has a third limb in addition to the above-described limbs,which third limb is at an angle to the first limb and/or the second limband has a third coupling region, preferably at the outer side thereof,by means of which the holding element is coupleable to the base. By wayof example, the angle of the third limb to the other two limbs imagesthe angle at which a third rotational axis of a rotational device is inrelation to the other two rotational axes.

In one variant, an above-described angle support has a third limborthogonal to the two other limbs, wherein the three limbs can beconnected to form a semi-cube. Each one of the limbs, or each one of thesides of a semi-cube, has a coupling region at the outer side. Such asupport design is advantageous in the case of three-axis rotary pivotjoints.

In a further variant, the support has an angled shape and the first, thesecond and the third limb are arranged in a C-shaped manner, wherein thelimbs are e.g. at right angles to one another.

In one embodiment, coupling means are arranged at the coupling regions.Preferably, the first coupling region has first coupling means and thesecond coupling region has second coupling means. If a third couplingregion is present, third coupling means are preferably arranged thereat.

The coupling means are preferably attached to the above-describedsupport, for example at the outer sides of the support, in particular atouter sides of limbs of an above-described angle support.

The coupling means, which are also referred to as coupling elements, arepreferably connectable to holding elements arranged on the base, in aninterlocking manner. Here, one or more degrees of freedom of movementcan be kept free, for example in order to enable a thermal expansion ofthe holding element, in particular of the support.

In one embodiment, one or more of the coupling regions are configured asa three-point bearing. A three-point bearing can be formed from threebearing means, e.g. spheres, bolts or pins. In particular, the firstcoupling means and/or second coupling means and/or third coupling meansetc. are configured as a three-point bearing or are part of athree-point bearing. A three-point bearing can be embodied by spheres,which engage on the opposite side (base) in respectively one depression,or, in particular, engage in roller pairs or triple spheres, which arearranged on the base.

In an advantageous variant, the three-point bearing is configured insuch a way that

-   -   a first bearing means on the side of the support, for example a        sphere, engages in a depression arranged on the side of the        base, which depression does not enable a lateral degree of        freedom of movement, that is to say, for example, it engages        into a triple sphere,    -   a second bearing means on the side of the support, for example a        sphere, engages in a depression arranged on the side of the        base, which depression enables a lateral degree of freedom of        movement, that is to say, for example, it engages into a roller        pair, and    -   a third bearing means on the side of the support, for example a        sphere or a screw tip, impacts on a planar or substantially        planar surface on the base, for example it impacts on a        hard-metal disk attached to the base.

What is ensured in this embodiment is that a possibly present thermalexpansion of the support always occurs in two defined directions.

Preferably, a tensile force is generated between the holding element andthe base, which is also referred to as “pretensioning”. Such a tensileforce can prevent the holding element from jumping out of a bearing.Depending on the orientation of the holding element and a rotationaldevice fastened thereto, jumping out of the bearing can be broughtabout, for example, by the weight thereof or by a movement of theholding element if the base is e.g. a rotary plate of a reference rotarytable, as described in the exemplary embodiments, or of parts of therotational device.

The pretensioning increases the reproducibility of the orientation ofthe holding element and a rotational device attached thereto. Apretension can be implemented e.g. magnetically, preferably at a centralpoint between a plurality of bearing points, or by the inherent weightof the holding element. An additional mass can be attached to theholding element in order to increase the mass of the holding element.For the purposes of magnetic pretension, the holding element can have amagnet which, for example, can be installed or set into the holdingelement. Such a magnet can exert an attractive force to a ferromagneticsubstrate, for example to a ferromagnetic base. The pretension can alsobe advantageous if large accelerations occur when qualifying therotational axis, for example as a result of release movements in thecase of latching rotary pivot joints. Further means for pretensioningare screws, hooks, a bayonet or a spring.

Instead of a three-point bearing, the holding element can also be fixedlocally to the base in a different manner, for example by means of oneor more stops, hooks, screws, latching means, etc.

One or more of the coupling regions can have one or more adjustmentmeans for adjusting the alignment of the holding element on the base.Examples of this are screw drives, such as set screws, leveling screws.An adjustment means can also simultaneously be a bearing means, forexample of a three-point bearing. By way of example, one of the bearingpoints can be a tip of a leveling screw which lies on a counter-face onthe base.

The one or more adjustment means may for example set the coaxialitybetween a rotational axis of the rotational device and the rotationalaxis of a reference rotary table if a method for determining therotational position error of the rotational device is intended to beperformed, which method is still described below and in the exemplaryembodiments.

The holding element has a holder for holding the rotational device,which is fastened to the support. The holder is preferably configured insuch a way that a rotational device with a connection point providedthereon is connectable to the holder in a fitting manner. A connectionpoint of the rotational device is a mechanical and, preferably, also anelectrical interface of the rotational device, by means of which therotational device can be assembled in a coordinate measuring machine ora machine tool. By way of example, a rotary pivot joint for a coordinatemeasuring machine is connected to a holder on the side of the coordinatemeasuring machine which, for example, is provided on a sleeve. Aconventional interface at a rotational device has, as mechanicalelements, a three-point bearing, for example three pairs of spheres,into which respectively one roller on the side of the CMM, in particularat a sleeve, engages, and electrical contacts. The holder of the holdingelement according to the invention can be configured in a manneridentical to a holder, at least in mechanical terms, which holder isprovided for fastening the rotational device to a CMM, preferably alsoin a manner identical in terms of the electrical and, to the extent thatthese are present, also pneumatic contacts. In other words, the holdingelement according to the invention has an interface in the form of aholder which is identical to the interface at a CMM, at which therotational device is attachable for the purposes of the measurementoperation.

The holding element can have different holders, which are configured inthe form of different interfaces. Thus, it is possible to attachdifferent rotational devices with in each case a different (counter)interface at the holding element. In the case of an angle-shapedsupport, different holders or different interfaces can be attached e.g.to different limbs of the support, in particular on the inner sides ofthe limbs. Accordingly, as described above, a third holder, which inturn is configured as another interface, can be attached to a thirdlimb.

In one embodiment, the holding element has one or more apparatuses forsupplying energy to the rotational device or to the sensor arrangement.Examples of this are electrical connections and/or electrical lines, bymeans of which and as a result of which a rotational device or sensorarrangement fastened to the holding element can be supplied with energyin order to bring about a rotation of parts of the rotational device. Byway of example, contacts and/or lines can be arranged in/on the support.

In a specific embodiment, the apparatus for supplying energy is arrangedin a coupling region of the holding element or in a plurality ofcoupling regions, in particular on one or more outer sides of thesupport. The following description of the apparatus relates to onecoupling region. An apparatus for supplying energy can be embodiedanalogously for other coupling regions.

In one variant, the apparatus for supplying energy has a first elementof a first plug-connection, which is arranged in the coupling region andconnectable to a second element of the first plug-in connection, whichis arranged on the base. The elements of the plug-in connectionpreferably have one or more electrical contact points.

The apparatus for supplying energy can have a first element of a secondplug-in connection, which is arranged on the support on the side of theholder for the rotational device and connectable to a second element ofthe second plug-in connection, which is arranged on the rotationaldevice or on the sensor arrangement. The elements of the plug-inconnection preferably have one or more electrical contact points.

The apparatus for supplying energy can have one or more contacts orcontact points which are respectively connectable to one or more countercontact points or counter contacts which are arranged on the base,wherein energy is supplied to the rotational device via the countercontacts which are arranged on the base. In one variant, one or more ofthe contact points simultaneously also form a bearing means of athree-point bearing, which was already described above. Here, a bearingmeans of a three-point bearing serves not only for mechanically bearingthe holding element on the base but also as a contact for supplyingenergy to the rotational device attached to the holding element for thepurposes of operating the rotational device. By way of example, abearing means in the form of an electrically conductive sphere or anelectrically conductive screw can also simultaneously serve aselectrical contact point.

One or more supply lines can be arranged on or in the support of theholding element, which supply lines extend from the contact/bearingmeans to the holder for the rotational device. In the holder, the supplyline or lines can in turn lead to one or more contact points, at whichthe rotational device is connected. The contact points at the holder canbe part of an above-described interface for attaching the rotationaldevice. Supply line or lines can likewise be arranged in or on the base,which conduct current from an external current source to the countercontact points on the base.

In one embodiment of the invention, the holding element has one or moreidentification means, which serve to identify the orientation of theholding element on the base. Instead, or additionally, the one or moreidentification means can also be configured to identify the type of therotational device or the sensor arrangement. By way of example, usingthe identification means, it is possible to identify whether therotational device is a rotary table or a rotary pivot joint and/or it ispossible to identify the type of rotary table or rotary pivot joint. Byway of example, it is possible to identify what sensors the sensorarrangement has and/or in what spatial orientations individual sensorsare arranged. Examples of identification means are a barcode, a QR ormatrix code, or a sensor system. By way of example, a sensor system canbe embodied as reflectors or switching cams or dry reed contacts orradiofrequency identifiers (RFID), by means of which an identificationof the orientation is made possible. It is possible to integrate such asensor system into a three-point bearing. Contact points of the bearingcan serve as contacts for an identification means, or an identificationmeans can be arranged in the center of a three-point bearing.

With the aid of the identification means it is possible, for example, toautomatically activate test plans that fit to the respective axis whenqualifying an axis of the rotational device and/or assign theestablished correction values to the fitting axis. The identificationmeans can also be configured—either solely for this purpose or as anadditional feature—in such a way that it is possible to distinguishbetween different types of a holding element or support or identify aspecific type, for example a type which has a fitting embodiment for aspecific rotational device.

In one embodiment, the support of the holding element has one or moreapertures for passing measuring radiation. If the holding element isrotated relative to a radiation-emitting sensor, such as anautocollimator or laser distance sensor, during a measurement, parts ofthe support can cover the measurement beam in specific rotationalpositions, which is why such a passage opening is advantageous. Inparticular, a support can have limbs and one or more apertures can bearranged in each case in one or more of the limbs.

In a further aspect, the invention relates to an arrangement comprising

-   -   a holding element as described above,    -   a first rotational device or a sensor arrangement, which is held        by the holding element,    -   a base, which is configured for coupling on the holding element        in at least two different, preferably reproducible poses,        wherein a pose is defined by the orientation and position of the        holding element.

The arrangement can have a movement error establishment apparatuscomprising at least one measuring sensor, which is configured to measurea measurement variable which enables an establishment of rotationalerrors of the rotational device, wherein the holding element is tuned toa rotational device to be held, in such a way that the at least onemeasuring sensor is able to measure the measurement variable, e.g.without the position and orientation of the measuring sensor changing,relative to the base, when the holding element with the held rotationaldevice is in a first one of the preferably reproducible poses and ableto measure the measurement variable when the holding element with theheld rotational device is in a second one of the preferably reproducibleposes. A rotational position establishment apparatus, which issubsequently still described on the basis of a method for establishing arotational position error of a rotational device, is a specific movementerror establishment apparatus. In the method, a rotational device iscoupled to a reference rotational device. Specifically, the base is therotary plate of a reference rotary table, the rotational position orchange in rotational position of which is known accurately. If therotational device is positioned on a reference rotational device bymeans of the holding element, a specific method for establishingrotational errors, in particular the rotational position error, can becarried out by the rotational device, which is described in more detailbelow and in the examples.

Furthermore, in addition to the aforementioned elements, the arrangementcan also have a test body which is connected to the rotational device. Atest body will still be described below and can be attached to therotational device for the purposes of qualifying a rotational axis ofthe rotational device. A qualification method using the test body willstill be described below and in the examples.

In the arrangement according to the invention, an XY-table and/or a tilttable can be attached between the holding element, in particular thesupport thereof, and the base, as a result of which it is possible toorient the holding element and the rotational device fastened thereto.

The arrangement can furthermore have an adjustment device for adjustingor displacing the holding element together with the rotational device.Using this, it is possible to perform a collision-free positioning ofthe holding element together with the rotational device on the base. Byway of example, an adjustment device can linearly displace the holdingelement on the base if the bearing is configured in such a way that itpermits linear guiding. By way of example, in the case of a V-shapedbearing, in which a V-guide is attached to the base, the holding elementcan be displaced in the V-shaped guide.

The holding element and the rotational device can be positioned and/orrotated from one orientation to any other orientation by hand or by arobot or by any other actuators, e.g. by pneumatic actuators.

For different installation lengths of rotational devices, for examplefor rotary pivot joints which are the same per se but have differentlengths, the base can be provided with a plurality of alternativebearing points and/or the base can e.g. have a plurality of bearingmeans for bearings at different positions such that the holding elementtogether with the rotational device can be positioned on the base atdifferent positions.

Under III, the following subject combinations are also disclosed,wherein the specified reference signs establish a reference to thefigures in merely an exemplary manner for explanation purposes.

-   1. A holding element (50; 510; 520) for holding a rotational device    (2) which has a part rotatable in relation to a rotational axis or    which has a plurality of parts (66, 67) rotatable about rotational    axes (A, B), or for holding a sensor arrangement (750) which has a    plurality of sensors (73, 74, 75, 76, 77), wherein the sensors are    configured to measure deviations in respect of at least one degree    of freedom of movement of the rotational device,    -   wherein the holding element comprises:        -   a first holder (68) for holding the rotational device (2) or            sensor arrangement (750),        -   a support (51, 52), to which the first holder (68) is            fastened, wherein the support (51, 52) has at least a first            coupling region (90; 901) and a second coupling region (91;            902), by means of which the holding element (50; 520) is            coupleable to a base (61; 611), and    -   wherein the first coupling region (90; 901) is configured to        couple the holding element (50; 520) in a first position and/or        orientation to the base (61; 611) such that the sensor        arrangement (750) or rotational device (2) held by the holding        element (50; 520) is arranged in a first position and/or        orientation when coupling the first coupling region (90; 901) to        the base (61; 611), and    -   wherein the second coupling region (91; 902) is configured to        couple the holding element (50; 520) in a second position and/or        orientation to the base (61; 611) such that the sensor        arrangement (750) or rotational device (2) held by the holding        element (50; 520) is arranged in a second position and/or        orientation when coupling the second coupling region (91; 902)        to the base (61; 611).-   2. The holding element as claimed in point 1, wherein the first    orientation, in which the rotational device (2) is arranged,    corresponds to a predetermined orientation of a first rotational    axis (A) of the rotational device (2) and the second orientation, in    which the rotational device (2) is arranged, corresponds to a    predetermined orientation of a second rotational axis (B) of the    rotational device (2),    -   and so respectively one rotational axis of the rotational device        (2) is aligned in the predetermined orientation thereof when        coupling the first coupling region (90) to the base (61) and        when coupling the second coupling region (91) to the base (61).-   3. The holding element as claimed in point 1 or 2, wherein the first    coupling region (90) has first coupling means (55, 56, 58; 692, 693,    694) and the second coupling region (91) has second coupling means    (53, 54, 57; 692′, 693′, 694′).-   4. The holding element as claimed in one of the preceding points, in    which the first coupling means (55, 56, 58; 692, 693, 694) and/or    the second coupling means (53, 54, 57; 692′, 693′, 694′) form a    three-point bearing or are part of a three-point bearing.-   5. The holding element (510) as claimed in one of the preceding    points, wherein the support has a third coupling region (92), by    means of which the holding element (510) is coupleable to the base    (61),    -   wherein the third coupling region (92) is configured to couple        the holding element (50) in a third position and/or orientation        to the base (61) such that the sensor arrangement (750) or        rotational device (2) held by the holding element (50) is        arranged in a third position and/or orientation when coupling        the third coupling region (92) to the base (61).-   6. The holding element (50; 510) as claimed in one of the preceding    points, wherein the support (51, 52) has a first limb (51) and a    second limb (52) which are at an angle to one another, wherein the    first holder (68) is fastened to one of the limbs and wherein the    first limb (51) has the first coupling region (90) and the second    limb (52) has the second coupling region (91).-   7. The holding element (510) as claimed in points 6 and 5, wherein    the support (51, 52, 511) has a third limb (511) which is at an    angle to the first limb (51) and/or the second limb (52), wherein    the third limb (511) has the third coupling region (92).-   8. The holding element (50; 510) as claimed in one of the preceding    points, in which one or more of the coupling regions (90, 91; 90,    91, 92) have one or more adjustment means (57, 58; 57, 58, 514) for    adjusting the location of the holding element (50; 510) on the base    (61).-   9. The holding element as claimed in one of the preceding points,    comprising one or more apparatuses for supplying energy (69; 690,    691′) to the rotational device (2) or the sensor arrangement (750).-   10. The holding element as claimed in point 9, wherein the apparatus    for supplying energy (690) is arranged in a coupling region (90, 91)    or respectively one apparatus for supplying energy (690) is arranged    in a plurality of coupling regions (90, 91).-   11. The holding element as claimed in point 9 or 10, wherein the    apparatus for supplying energy has a first element (690) of a first    plug-connection, which is arranged in the coupling region and    connectable to a second element (691) of the first plug-in    connection, which is arranged on the base (61).-   12. The holding element as claimed in one of points 9-11, wherein    the apparatus for supplying energy has a first element (691′) of a    second plug-in connection, which is arranged on the support (51, 52)    on the side of the first holder (68) and connectable to a second    element (690′) of the second plug-in connection, which is arranged    on the rotational device (2) or on the sensor arrangement (750).-   13. The holding element as claimed in one of the preceding points,    comprising one or more identification means for identifying the    orientation of the holding element (50) on the base (61) and/or for    identifying the type of the rotational device (2) or of the sensor    arrangement (750).-   14. The holding element as claimed in one of the preceding points,    which has one or more further holders for further rotational devices    or sensor arrangements in addition to the first holder (68).-   15. The holding element as claimed in one of the preceding points,    wherein the support (51, 52, 511) has one or more apertures (515)    for passing measuring radiation (S).-   16. An arrangement comprising    -   a holding element (50; 510) as claimed in one of the preceding        points,    -   a first rotational device (2) or a sensor arrangement (750),        which is held by the holding element (50; 510),    -   a base (61), which is configured for coupling on the holding        element (50; 510) in at least two different poses, wherein a        pose is defined by the orientation and position of the holding        element.-   17. The arrangement as claimed in point 16, wherein the base (61) is    a rotatable part of a second rotational device (60).-   18. The arrangement as claimed in point 16 or 17, wherein the first    rotational device (2) is a rotary table, a rotary joint with one    rotational axis or a rotary pivot joint with two or more rotational    axes.-   19. The arrangement as claimed in one of points 16-18, wherein the    arrangement has a movement error establishment apparatus comprising    at least one measuring sensor (88) which is configured to measure a    measurement variable which enables an establishment of rotational    errors of the rotational device (2),    -   wherein the holding element (50) is tuned to a rotational device        (2) to be held, in such a way that the at least one measuring        sensor (88) is able to measure the measurement variable when the        holding element (50) with the held rotational device (2) is in a        first one of the poses and able to measure the measurement        variable when the holding element (50) with the held rotational        device (2) is in a second one of the poses.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

The invention will be described below on the basis of examples. Indetail:

FIG. 1 shows a schematic diagram of an arrangement for carrying out themethod according to the invention,

FIG. 2 shows a test body usable for the method, comprising a mirroraligned in a manner perpendicular to the rotational axis and a doublesphere standard aligned in a manner coaxial with the rotational axis,

FIG. 3 shows a test body usable for the method, comprising a mirroraligned in a manner perpendicular to the rotational axis and a cylinderaligned in a manner coaxial with the rotational axis,

FIG. 4 shows a test body usable for the method, comprising two mirrors,aligned to one another and in a manner orthogonal to the rotationalaxis, as test elements and a sphere, which is arranged centrally on therotational axis,

FIG. 5 shows a test body usable for the method, comprising a mirroraligned in a manner perpendicular to the rotational axis as a testelement and a sphere arranged centrally on the rotational axis and afurther mirror oriented in the direction of the rotational axis as atest element,

FIG. 6 shows a test body usable for the method, comprising two mirrors,preferably aligned to one another and in a manner orthogonal to therotational axis, as test elements,

FIG. 7 shows a test body usable for the method, comprising a sphere as atest element, which is assembled in the plane orthogonal to therotational axis at a radius >0, and a double sphere standard aligned ina manner coaxial with the rotational axis,

FIG. 8 shows a test body usable for the method, comprising a mirror as atest element, which is assembled in the plane orthogonal to therotational axis at a radius >0,

FIG. 9 shows a setup with a test body and an autocollimator withmultiple evaluation,

FIG. 10 shows an example for an arrangement with a two-axis rotary pivotjoint and a test body for carrying out the method according to theinvention,

FIG. 11 shows an example for a further arrangement with a two-axisrotary pivot joint and a test body for carrying out the method accordingto the invention,

FIG. 12 shows an example for an arrangement with a two-axis rotary pivotjoint and a test body for performing the method according to theinvention and for determining further translational and rotationaldeviations,

FIG. 13 shows an example for an arrangement with a rotary table and atest body for carrying out the method according to the invention and fordetermining further translational and rotational deviations,

FIG. 14 shows an arrangement with a rotational device and a referencerotational device,

FIG. 15 shows an arrangement with a rotational device and a referencerotational device,

FIG. 16 shows an arrangement with a rotational device and a referencerotational device,

FIG. 17 shows an arrangement with a rotational device and a referencerotational device,

FIG. 18 shows an arrangement with a rotational device and a referencerotational device,

FIG. 19 shows an arrangement with a rotational device and a referencerotational device,

FIG. 20 shows an arrangement with a rotational device and a referencerotational device,

FIG. 21 shows an arrangement with a rotational device and a referencerotational device,

FIG. 22 shows an arrangement with a rotational device and a referencerotational device,

FIG. 23 shows an arrangement with a rotational device and a referencerotational device,

FIG. 24 shows an arrangement for undertaking a flipping-over measurementusing the method according to the invention,

FIG. 25 shows an error correction curve from a flipping-overmeasurement,

FIG. 26 shows an error correction curve from a flipping-overmeasurement,

FIG. 27 shows an embodiment of a holding element, arranged in ameasurement setup,

FIG. 28 shows a first element for a plug-in connection for connecting aholding element to a base or for connecting a rotational device to aholding element,

FIG. 29 shows a second element for a plug-in connection for connecting aholding element to a base or for connecting a rotational device to aholding element,

FIG. 30 shows a holding element with a sensor arrangement attachedthereto, in a first position and orientation, and

FIG. 31 shows a holding element with a sensor arrangement attachedthereto, in a second position and orientation.

DESCRIPTION OF THE INVENTION

A possible setup for the course of the error registration is shown inFIG. 1: a rotational device 201 is placed onto a reference rotationaldevice 60, in this case a rotary table which has a lower part 62 and arotary plate 61. In this example, the rotational device 201 is likewisea rotary table, in the rotational angle measuring system of which (notdepicted here) the rotational angle error is intended to be established.The rotary table 201 has a lower part 205 and a rotary plate 206. Thelower part 205 of the rotary table 201 is placed onto the rotary plate61 of the reference rotational device 60. The lower part 205 isconnected in a conjointly rotating manner to the rotary plate 61 due tothe friction between the plate 61 and the lower part 205 and theinherent weight of the rotary table 201. The plate 61 of the referencerotary table 60 is rotatable relative to the lower part 62 about theaxis R of the reference rotational device. The plate 206 of the rotarytable 201 is rotatable relative to the lower part 205 about the axis D.The axes D and R are arranged in a substantially coaxial manner.

A mirror is arranged on the plate 206 of the rotary table 201 as a testelement 5, which mirror is aligned in the direction of an autocollimator(AKF) 88. The measurement beam S of the AKF 88 impinges on the surfaceof the mirror 5.

The order in which the reference rotational device 60, the rotationaldevice 201 and the mirror 5, with an associated AKF 88, are in relationto one another is variable. It would also be feasible for the AKF 88 tostand on the rotational device 201 and for the mirror 5 to be fastenedexternally. Moreover, the reference rotational device 60 could stand onthe rotational device 201, for example when calibrating a very largerotational device 201.

FIG. 1 furthermore shows an error establishment apparatus 1001, whiche.g. is a computing unit, in particular a computer, which can perform acalculation according to a given program flow. In addition to errorestablishment, the computer 1001 can also be used to transmit controlsignals to the stator 205 of the rotary table 201 and to the stator 62of the reference rotary table 60, in particular signals for controllingthe movements of the rotors 61 and 206. In addition to errorestablishment, the measurement signals from the stator 205 of the rotarytable 201 and from the stator 62 of the reference rotary table 60 canalso be transmitted to the computer 1001, in particular measurementsignals which provide information about the rotational position of therotors 61 and 206. A cable 801 serves to transmit signals from thestator 205 of the rotary table 201 to the error establishment apparatus1001 and a cable 802 serves to transmit signals from the stator 62 ofthe reference rotary table 60 to the error establishment apparatus 1001.Furthermore, the cables 801 and 802 also serve to transmit energy.Naturally, a plurality of cables could also be provided in each caseinstead of respectively one cable 801 or 802, for example one for signaltransmission and one for energy transmission. What is not shown in thisand in subsequent figures are signal and energy transmission apparatusesto an AKF or to sensors and further control or evaluation apparatuses.Furthermore, user interfaces at the only schematically depicted computer1001 and a display are not depicted.

Below, possible embodiments of the method are described. The rotationalposition error of the rotational position establishment system of therotary table 201 is intended to be established.

The plate 61 of the reference rotary table 60 is positioned in relationto the lower part 62 in such a way that the rotational positionestablishment system of the reference rotary table 60 is at thereference or zero marker thereof. Likewise, the plate 206 of the rotarytable 201 is positioned in relation to the lower part 205 in such a waythat the rotational position establishment system of the rotary table201 is at the reference or zero marker thereof. Instead of the zeromarkers, any other rotational position can be used as first rotationalposition.

Now, the rotational positioning angle of the mirror 5, which is referredto as offset angle below, can be registered using the AKF 88 or,alternatively, a different angle measuring instrument. In a specialcase, the offset angle can also be zero, i.e. no offset would be presentin this case.

For the error registration of the rotational position establishmentsystem of the rotary table 201, support points for the errorregistration are initially defined. Here, these can be distributedirregularly and also regularly on one or more rotations of the plate 61of the reference rotary table 60, wherein the variant of the integerdivisors of 360° is preferred as an increment to be selected. As aresult of this, errors from a badly set measuring system remainunconsidered.

Whether the plate 61 is rotated in a positive or negative direction asobserved from above is not decisive for the method, i.e. both variantsare of equal value. However, they can be twisted in the positive andnegative rotational directions in order to determine hysteresis effects.

For a negative rotational direction of the plate 61, the rotationalangle positions (intended positions) to be approached in the case of sixsteps for the reference axis would be e.g. 0°, −60°, −120°, −180°, −240°and −300°. However, the number can be increased almost as desired, forexample if short-periodic errors of the rotational axis to be calibratedare intended to be registered or if aliasing effects are intended to beprevented.

When varying the rotational position of the plate 61 of the referencerotary table 60 and of the plate 206 of the rotary table, one of thefollowing positioning strategies is preferably applied:

Variant 1 of the Method:

Variant 1 is a special example of variant d), which was described in thegeneral description. For the respective support point, the settings areundertaken as follows:

The plate 61, which is also referred to as rotor, of the referencerotary table 60 is positioned at a negative predetermined intendedrotational position, in this case e.g. −60°. This is the changedrotational position of the reference rotational device mentioned in thegeneral part of the description, i.e. the changed rotational position ofthe third part 61 (in this case the plate) and fourth part 62 (in thiscase the lower part 62, also referred to as stator) relative to oneanother, obtained by varying the rotational position of the referencerotary table 60.

The changed rotational position of the reference rotational device isaccurately known because the angle measuring system of the referencerotary table 60 is calibrated. Below, this variable will be denoted asX.

The plate 206 of the rotary table 201, also referred to as rotor of therotary table 201, is positioned on the negated value of the intendedrotational position of the reference table, in this case +60°, whereinthe negative intended position is set with the aid of theerror-afflicted rotational position establishment system of the rotarytable 201. This is the changed rotational position of the rotationaldevice 201 mentioned in the general part of the description, i.e. thechanged rotational position of the first part (in this case the plate206) and second part (in this case the lower part 205, also referred toas stator) relative to one another, obtained by varying the rotationalposition of the rotary table 201.

The changed rotational position of the rotational device is indicated bythe rotational position establishment system, the error of which isintended to be determined. Below, this variable will be denoted as Y.

If the rotational position establishment system of the rotary table 201is error afflicted, i.e. if the real rotational angle deviates from+60°, then the consequence thereof is that the relative rotationalposition of the first part 206 and of the fourth part 62 relative to oneanother has changed compared to the initial state. As described above,in the initial state, the offset angle of the mirror 5 was establishedusing the AKF 88, wherein the offset angle can also be zero in thespecial case. The change in the relative rotational position of thefirst part 206 and of the fourth part 62 relative to one another, whichis denoted as variable Z, corresponds to the following:Z=angle established by the AKF after varying the rotationalpositions−offset angle

The rotational position error F (in this case the angle position error)of the rotational position establishment system of the rotary table 201is established using the error establishment apparatus 1001.

In this example, the rotational position error corresponds to: F=Z.

Thus, the rotational position error in the special variant 1 correspondsto the difference between the angle registered by the AKF 88 and theoffset angle of the mirror mentioned above. The nominal(error-afflicted) rotary angle of the first part 206 and of the secondpart 205 in relation to one another (Y) and the nominal rotational angleof the third part 61 and of the fourth part 62 relative to one another(X) add to zero. The nominal rotational angle means the displayed angle,which in this case is based upon a default value.

In another variant of the method, it is also possible to select thenominal angles X and Y in such a way that they do not add to zero and toimplement the rotational positions of the rotational device and thereference rotational device in such a way that the rotational positionof the first part 206 and of the fourth part 62 relative to one anotherhas changed compared to the initial state, i.e. so that the AKF measuresan angle deviation Z. Then, the error F emerges from:F=Z−(difference between the nominal angles X and Y)Variant 2 of the Method:

Variant 2 is a special example of variant e), which was described in thegeneral description.

The plate 61 of the reference rotary table is positioned at a negativepredetermined intended rotational position, e.g. −60°. This is thechanged rotational position of the reference rotational device mentionedin the general part of the description, i.e. the changed rotationalposition of the third part 61 (in this case the plate) and the fourthpart 62 (in this case the lower part) relative to one another, which isaccurately known because the angle measuring system of the referencerotary table 60 is calibrated. Below, this variable will be denoted asX.

The plate 206 of the rotary table 201 is positioned in such a way thatthe angle measured by the external AKF 88 corresponds exactly to theoffset angle measured prior to varying the rotational positions. Thismeans that the rotational position of the mirror 5 relative to the AKF88 is unchanged compared to beforehand (before varying the rotationalpositions). This means, furthermore, that the resultant rotationalposition of the first part 206 and of the fourth part 62 is unchanged orsubstantially unchanged. Therefore, in the ideal case, the angle valuedisplayed by the AKF minus the previously determined offset is zero. Ingeneral, the ideal case is not achieved due to measuring errors orsetting inaccuracies, which is why, in the real case, the angle valuedisplayed by the AKF minus the previously determined offset variesslightly around zero within the scope of the measuring error or thesetting inaccuracy.

The angle Y, which emerges from the above-described settings, is readoff at the rotational position establishment system. The setting of therotary table corresponds to the changed rotational position of therotational device mentioned in the general part of the description, i.e.the changed rotational position of the first part (in this case theplate 206) and the second part (in this case the lower part 205)relative to one another, displayed by the rotational positionestablishment system, the error (F) of which is intended to bedetermined. The angle position of the plate 206 of the rotary table 201to be calibrated corresponds to:Y=+60°+rotational position error of the rotational positionestablishment system of the rotary table 201Y=−X+F.

The rotational position error F (in this case the angle position error)of the rotational position establishment system of the rotary table 201is established using an error establishment apparatus 1001. Therotational position error F corresponds to:F=X+Y,where Y corresponds to the nominal angle value displayed by theerror-afflicted measuring system,i.e. the sum of the rotational angles which are displayed by therotational position establishment system of the reference rotary table60 and the rotational position establishment system of the rotary table201. In contrast to variant 1, Z remains unconsidered in the calculationsince the value is (approximately) zero.Variant 3 of the Method:

Variant 3 is a special example of variant e), which was described in thegeneral description.

The plate 206 of the rotary table 201 is positioned at a positivepredetermined intended rotational position, e.g. +60°, displayed by the(error-afflicted) rotational position establishment system of the rotarytable 201. This is the changed rotational position of the rotationaldevice mentioned in the general part of the description, i.e. thechanged rotational position of the first part 206 (in this case theplate) and the second part 205 (in this case the lower part) relative toone another. Below, this variable will be denoted as Y.

The plate 61 of the reference rotary table 60 is positioned in such away that the angle measured by the external angle measuring instrument88 corresponds exactly to the previously measured offset angle. Thismeans that the rotational position of the mirror 5 relative to the AKF88 is unchanged compared to beforehand (before varying the rotationalpositions). This means, furthermore, that the resultant rotationalposition of the first part 206 and of the fourth part 62 is unchanged.

The angle X which emerges from the above-described settings is read offat the calibrated angle measuring system of the reference rotary table60. The setting of the reference rotary table corresponds to the changedrotational position of the reference rotational device 60 mentioned inthe general part of the description, i.e. the changed rotationalposition of the third part (in this case the plate 61) and the fourthpart (in this case the lower part 62) relative to one another, displayedby the calibrated angle measuring system. The angle position of theplate 61 of the reference rotary table 60 corresponds to:X=−60°+rotational position error of the rotational positionestablishment system of the rotary table 201=−Y+F.

The rotational position error F (in this case the angle position error)of the rotational position establishment system of the rotary table 201is established using an error establishment apparatus (not shown here).The rotational position error corresponds to:F=X+Y,i.e. the sum of the rotational angles which are displayed by therotational position establishment system of the reference rotary table60 and the rotational position establishment system of the rotary table201, like in the above-described variant 2. In contrast to variant 1, Zremains unconsidered in the calculation since the value is zero.

In all variants, further angles can be set in further method steps andother rotational directions can be selected.

Variants 1-3 listed in an exemplary manner above differ as follows:

Variant 1 offers a speed advantage over variant 2 and variant 3 since,in variants 2 and 3, the rotational position of the rotational axis tobe calibrated or of the reference axis must be adjusted to an externalreference. Adjustment to a rotational position of the inherent measuringsystem is generally quicker. However, when applying variants 2 and 3,there is independence from the accuracy of the external angle measuringinstrument (AKF) since positioning is always to the same (possiblyinaccurate) displayed angle. However, there is dependence on thereproducibility of the AKF measuring system.

FIG. 2 shows a test body 1 which is connected to a rotary pivot joint 2.The test body 1 has a cylinder-rod-shaped holder 3 and a pedestal 4. Therotational axis B denotes one of the rotational axes of the rotary pivotjoint 2. The cylinder-rod-shaped holder 3 has a rotational symmetry andthe axis of rotational symmetry of the holder 3 is arranged in a mannercoaxial with the rotational axis B. However, this is not necessary inall cases, as shown on the basis of FIG. 11, where the axis ofrotational symmetry of the holder 3 is not coaxial with the rotationalaxis A of the rotary pivot joint in that case. Furthermore, the holder 3need not have rotational symmetry and can, in principle, have any crosssection. By way of example, the pedestal 4 is connected by way of athree-point bearing to the rotary pivot joint 2. The rotatable part ofthe rotary pivot joint 2, to which the pedestal 4 is attached and whichis rotatable in relation to the part 66 (see FIG. 12) is not visible: itlies within the part 66 (see FIG. 12) and is rotatable in relation tothe part 66 about the axis B. A mirror is attached laterally to therotational axis B as a test element 5 and connected to the holder 3 bymeans of a rod-shaped support 6. The reflection face 7 or the mirrorface faces away from the rotational axis B, points to the right in thisillustration and is aligned in the direction of an autocollimator 88. Inthe selected coordinate system, which is depicted on the right-hand sidein FIG. 2, the rotational axis B points in the Z-direction and themirror points in the X-direction in the shown position. When the holder3 is rotated about the rotational axis B, the mirror 5 rotates about thesame rotational angle as the holder 3 and the rotational angle isdetectable by means of the autocollimator 88 (abbreviated to AKF below).The rotations may be only very small. Two spheres 8, 9 as rotationallysymmetric elements are attached to the holder 3. Both spheres 8, 9 arealigned in a manner coaxial with the rotational axis B, i.e. the axis ofrotational symmetry thereof is axially flush with the rotational axis B.However, this is not necessary in all cases, as is shown on the basis ofFIG. 11, where the spheres 8, 9 are not coaxial with the rotational axisA of the rotary pivot joint in that case. The spheres 8, 9 form a doublesphere pair. The holder 3 can have a two-part design, wherein one partextends e.g. from the pedestal 4 up to in front of the first sphere 8and a second part contains the first sphere 8 and the second sphere 9.The spheres 8, 9 can be probed using five distance sensors, as willstill be described below in FIGS. 12 and 13. By way of example, thedistance sensors can be capacitive sensors, eddy current sensors,magnetic field sensors, optical sensors, in particular interferometers,or mechanical inductive sensing units. Additionally, the tilt of themirror 5, both about the rotational axis B and the Y-axis, can beobserved by the AKF. The five distance sensors, which are stilldescribed on the basis of a subsequent example, enable a registration ofthe movement errors in the three translational spatial directions andthe tilt about the X-axis and Y-axis. When applying a method still to bedescribed below with a reference rotational axis rotating in theopposite direction, the AKF enables the registration of the rotationalposition error of the axis B. Additionally, one of the two tilt anglesof the axis B about the X-axis or Y-axis is obtained from themeasurement with the AKF, depending on how the AKF and mirror arealigned. In the shown illustration, the tilt angle could be measuredabout the Y-axis. In order to measure the tilt angle about the X-axis,the mirror would have to be aligned with the reflection face 7 in thedirection of the observer and the beam of the AKF would have to bedirected onto the mirror in the observation direction. Naturally, thetilt angles can be measured in succession after the setup has changed.The tilt angle or angles can be compared with the angle established byway of the distance sensors (yet to be described below), as a result ofwhich the measurement reliability is increased.

FIG. 3 shows a setup with a test body 101, wherein the reference signshave the same meaning as in FIG. 1; the difference here is that acylinder 10 with an end face registrable by sensors is used as arotationally symmetric element instead of the spheres 8, 9. The cylinder10 is a special case of a second rotationally symmetric measurement bodywithin the meaning of the general description of the invention. In thetest body 101, like in FIG. 2, there is no “first” measurement bodywithin the meaning of the general description of the invention (such afirst measurement body is shown in the form of a sphere in FIG. 7).Instead of a cylindrical form, the second measurement body 10 could alsohave the form of a cuboid, wherein, in the view of FIG. 3, the view ofthe observer would fall on one of the four side faces of the cuboid. Thecuboid 10 would be a special case of a second measurement body with aplurality of faces pointing in different directions, within the meaningof the general description of the invention.

Now, the installation of the test body 1 in a CMM and a method forestablishing the rotational position error and further translational androtational errors is initially described on the basis of FIGS. 10 to 12.

In the upper part, FIG. 10 shows the basic setup of test body 1, arotational device 2 and an AKF 88, which was already described in FIG.2. In this example, the rotational device 2, also referred to as a testobject, is a rotary pivot joint 2 attached to an angle-shaped holdingelement 50. The holding element 50 has a holder 68, at which therotational device 2 is attached. Furthermore, a current supply 69 isshown, by means of which the rotational device 2 is supplied withenergy. Alternatively, the supply of energy and sensor signals can alsobe implemented directly by way of a plug-in connection, as shown inFIGS. 28 and 29. Where applicable, the rotary pivot joint 2, togetherwith the holding element 50, can also be driven pneumatically,hydraulically or in any other way (not shown here). The angle has twolimbs 51, 52 which form a support, wherein the limbs are in each caseprovided with a three-point bearing on the outer side. Each three-pointbearing consists of two sphere-shaped elements and a knurled screw foradjustment purposes. Elements in the form of part of a sphere,preferably a hemisphere, are also possible. The hemisphere-shapedelements 53 and 54, which form coupling means, are attached to the lowerlimb 52, wherein only the front sphere-shaped element is visible in theselected perspective. Provision is made for the end of a set screw 57 asa third point of the three-point bearing and as a further couplingelement. The hemisphere-shaped elements 53 and 54 and the end of the setscrew 57 lie in the second coupling region 91 of the holding element 50.The holding element 50 is coupled to the base by way of the secondcoupling region 91. In an analogous manner, the second limb 51 has twohemisphere-shaped elements 55, 56 as coupling elements, of which onlythe front one is visible in the selected perspective, and a set screw 58as a coupling element. In general, the coupling elements can also bereferred to as “bearing elements” and are also denoted in an abbreviatedmanner as “elements” in the examples. The hemisphere-shaped elements 55and 56 and the end of the screw 58 lie in the first coupling region 90of the holding element 50. The elements 53, 54, 55, 56 can be ahemisphere or else a whole sphere, which is partly sunk into the limb.

In the present figures, only one adjustment means in the form of a setscrew 57 or 58 is visible per coupling region. In order to set thecoaxiality with the reference rotational axis, respectively one furtherset screw, which is not shown here, can be provided in one or more ofthe coupling regions. In general, adjustment means can be present in anyexpedient number and combination. By way of example, one of thesphere-shaped elements 53, 54 or one of the sphere-shaped elements 55,56 can be replaced by a set screw. It is furthermore possible to combinea set screw with a sphere-shaped bearing element or a partialsphere-shaped bearing element, as shown in FIGS. 30 and 31. In thiscase, the set screw 57 and/or 58 would not taper as shown, but wouldhave a sphere or downward pointing hemisphere at the end, as is shown onthe basis of the set screws 585 and 586 in FIGS. 30 and 31. In general,a tapering bearing element or adjustment means is preferably used if thebearing is implemented on a smooth surface. A bearing element oradjustment means in the form of a (partial) sphere can advantageouslyinteract with a guide 63, 64, for example a roller pair or a triplesphere.

The three-point bearing of the angle-shaped holding element 50 enables avery accurate and reproducible orientation of the test body 1. Equippingtimes are minimized, particularly in the case of series measurements. Bymeans of the holding element 50, slightly different orientations of therotary pivot joint 2 can be established, as is identifiable whencomparing FIGS. 10 and 11 (bottom).

Depending on the spatial orientation of the test object 2, torques ordisplacements may occur, for example due to the weight of the test body1, of the test object 2 or, where applicable, due to the probing forces.In this case, deformations of the test object 2 or of the angled holderare eliminated by computation in a preferred variant.

In FIG. 10, the test object 2, in this case the rotary pivot joint 2,was placed onto a reference rotary table 60 together with the holdingelement 50, on the limb 51 of which the rotary pivot joint 2 isattached. The reference rotary table 60 has a rotary plate 61 and alower part 62, in relation to which the rotary plate 61 is rotatable.The rotational axis of the plate 61 is denoted by R. The referencerotary table 60 has the rotational axis R. The energy supply of thereference rotary table 60 is not depicted here. An orthogonal alignmentof rotational axes is not mandatory in this invention, neither ingeneral nor in the shown examples. The axes B and R in FIG. 10 could,for example, also be aligned horizontally, as could the axes A and R inFIG. 11, B and R in FIG. 12 and D and R in FIG. 13. A horizontalalignment of B and R in FIGS. 10 and 12 is advantageous to the extentthat, in the method described herein for recording the rotationalposition error (see below, for example), the rotary pivot joint 2 is inan orientation which corresponds to the orientation thereof in thesubsequent measurement operation in specific types of coordinatemeasuring machine, for example in the horizontal arm coordinatemeasuring machine type.

The holding element 50 is mounted on the plate 61 of the referencerotary table 60 by means of the three-point bearing thereof, consistingof the sphere-shaped elements 53, 54 and the knurled screw 57, and itrotates together with the plate 61. Guides 63, 64 (only the front guide63 is visible) for bearing the resting spheres 53, 54 are provided onthe plate 61 of the rotary table 60. By way of example, theschematically depicted guides 63, 64 can be roller pairs or triplespheres or a combination thereof. The guides 63, 64 ensure areproducible and constant positioning of the holding element 50 on therotary table 60.

The reference rotary table 60 has a calibrated rotary angle display. Asan alternative to the setup shown in FIG. 10, a test object 2 can alsobe placed directly on the reference rotary table 60, without use beingmade of a holding element 50 (compare FIG. 13, below, with a rotarytable as test object). It is possible to identify in the setup of FIG.10 that the rotational axis B of the test object 2 and the rotationalaxis R of the reference rotary table 60 are substantially flush orsubstantially coaxial with one another.

An exemplary method for recording the rotational position error of therotational axis B of the test object 2 is performed in the followingsteps:

-   (1) The plate 61 of the reference rotary table 60 and the test body    1 rotate incrementally in opposite directions, e.g. +3° and −3°.    Together with the plate 61, the holding element 50 and parts 66 and    67 of the rotary pivot joint 2 rotate e.g. by +3° about the axis R.    The test body 1 is rotated by −3° about the axis B relative to the    part 66 of the rotary pivot joint 2, with the relative rotation    being implemented between the pedestal 4 and the part 66.    -   From the position of the external observer, i.e. when observed        from the inert system, the mirror 5 thus remains stationary, or        substantially stationary, when both rotational axes rotate in an        ideal manner. After completing the movement step, the position        value of the mirror 5 is established using the AKF 88. In the        case of a rotational position error-free rotation about the axis        B, the position of the mirror 5 should remain constant. By        contrast, a deviating position of the mirror emerges as a result        of a rotational position error and the rotational position error        is determined with the AKF 88.-   (2) Step (1) is repeated with different angle values, preferably    until a multiple of 360° is obtained. In the case of roller-borne    parts that are rotatable relative to one another, it is advantageous    to acquire at least 2.5 rotations. Alternatively, the rotational    movement and the angle measurement with the AKF 88 can be    implemented continuously. Additional computational corrections can    also be undertaken in order to compensate for synchronization    problems. The great advantage of this method is that the increment    can be selected to be very small, i.e. even short-periodic error    components are registrable in a relatively short period of time.-   (3) Subsequently, the measurement of the remaining—in total    5—rotational and translational errors can occur. To this end, the    lower reference rotary table 60 is not rotated, i.e. the plate 61 is    fixed relative to the lower part 62 and only the test body 1 is    rotated relative to the part 66 of the rotary pivot joint 2 about    the axis B. A setup for recording further errors is explained in    FIG. 12.-   (4) Characteristic variables are calculated from the data obtained    and are compared to a given specification. Or correction values for    a CAA correction are established from the data.

In the case of rotational devices with a plurality of rotational axes(multi-stage rotational axes), steps (1)-(4) are repeated for eachrotational axis.

In alternative methods, it is possible initially to establish therotational position error and at least one further wobble error andsubsequently to establish the translational errors. Or the registrationof all degrees of freedom is implemented simultaneously. From this, thefollowing preferred requirements for the reference rotational axis Remerge:

-   -   If the errors Rb (rotational position errors of the axis B of        the test object 2) and the errors Tx, Ty, Tz (translational        deviation in the X-, Y- and Z-direction, respectively), Rx, Ry        (rotational deviations about the X-axis and Y-axis,        respectively) are established in succession, the reference        rotational axis R of the rotary table 60 should only have a        rotational position error that is as small as possible. A        rotation of the plate 61 about the reference rotational axis R        in relation to the lower part 62 could preferably only occur        when recording the Rb error, as explained above. However, if the        reference rotary table 60 has very small wobble and translation        components in relation to the rotational axis to be calibrated,        there can, however, also be a complete qualification of the        rotational axis to be calibrated when rotating the plate 61        about the R-axis in relation to the lower part 62. Minimizing or        eliminating the rotary position error of the reference        rotational axis R can be implemented, for example, by mechanical        precision, a highly accurate scale, a self-calibration method or        a CAA (computer aided accuracy) correction.    -   If the errors Rb, Rx, Ry are established simultaneously in a        first part of the method and if, subsequently, the errors Tx,        Ty, Tz are established simultaneously (or if Rb, Rx are        initially established simultaneously, followed, simultaneously,        by the errors Tx, Ty, Tz, Ry; or if Rb, Ry are established        simultaneously in a first part of the method and the errors Tx,        Ty, Tz, Rx are established simultaneously in a second part of        the method), the reference rotational axis R must have a        rotational position error that is as small as possible and a        wobble error that is as small as possible. The reference        rotational axis R would only move when recording the Rb, Rx, Ry        error. By way of example, a small wobble error can be achieved        by mechanical outlay, CAA corrections or a partial online        correction.    -   If all errors Rb, Rx, Ry, Tx, Ty, Tz are established        simultaneously, the reference rotational axis R must have        movement errors that are as small as possible in all 6 degrees        of freedom. By way of example, this can be achieved by        mechanical outlay, CAA corrections or a complete online        correction.

FIG. 11 shows a setup for determining the rotational position error ofthe A-axis of the rotary pivot joint 2. The second axis B, which wasmeasured using the setup according to FIG. 10, is plotted in FIG. 11 forcomparison purposes. In relation to the setup of FIG. 10, the holdingelement 50 was rotated by 90°. The holding element 50 is coupled to thebase by the first coupling region 90 or rests on the plate 61 of thereference rotary table 60 with a three-point bearing provided on thelimb 51 (instead of a three-point bearing provided at 52 like in FIG.10), without the rotational device 2 needing to be uninstalled. Thethree-point bearing brought about by the spheres 55, 56 and the knurledscrew 58 is implemented in an analogous manner to that in FIG. 10. Thetest body 1 was reconfigured and aligned along the rotational axis A ofthe rotary pivot joint 2.

The spheres 8 and 9 can be arranged flush with the axis A or not, as isshown here. If the plate of the reference rotary table 60 is rotatedabout the axis R during the qualification such that the positions of thetest body and of the mirror 5 remain unchanged, or substantiallyunchanged, as described above (plate 61 of the reference rotary table 60and the test body 1 rotate in opposite directions about the axis R orA), then the spheres need not necessarily lie flush. Then, the axis A ispreferably substantially coaxial or concentric to the axis R. Bycontrast, if no rotation is carried out about the axis R, the doublesphere 8, 9 is preferably arranged in a manner substantially concentricand coaxial to the axis A. If the plate 61 of the reference rotary table60 and the test body 1 rotate in the same direction about the axis R orA, then the double sphere 8, 9 is preferably arranged in a mannersubstantially concentric and coaxial to the axis A and the axis A ispreferably substantially coaxial or concentric to the axis R.

The test body 1 is fastened to the rotary pivot joint 2 using theadapter 65. The adapter 65 is held magnetically. Like in FIG. 10, theAKF 88 remains aligned with the mirror 5. The method for recording therotational position error about the axis A can be performed in ananalogous manner, as is described above in FIG. 10 for the case of theaxis B. However, in this case, the test body is not twisted relative tothe part 66, but the part 66 is rotated about the axis A in relation tothe part 67 and the test body 1 is not rotatable relative to the part66.

FIG. 12 shows the setup of FIG. 10 in a wider context and thepositioning of sensors for recording further translational androtational errors that occur when rotating the rotary pivot joint 2about the axis B. A stand 70 supports an arm 71, to which a sensorholder 72 with three walls perpendicular to one another is attached. Twodistance sensors 73, 74 which point to the spheres 8 and 9 in the Xdirection are attached to a first wall. Using the distance sensors, itis possible to register the translation error Tx and the rotationalerror Ry, which emerges during the rotation of the holder 3 about theY-axis. Distance sensors 75 and 76 which are aligned on the spheres 8and 9 in the Y-direction are attached to the rear-side wall of thesensor holder 72. Using the distance sensors 75 and 76, it is possibleto register the translation error in the Y-direction Ty and therotational error Rx. Using the distance sensor 77, which is aligned onthe upper sphere 9 in the Z-direction, it is possible to register thetranslation error in the Z-direction Tz. The spheres 8, 9 are a doublesphere pair. Alternatively, it is possible to use a cylinder, like inthe case of the test body 101 in FIG. 5, and equally arranged distancesensors can be directed onto the cylinder surface and the end face ofthe cylinder.

In FIG. 12, the rotary table 60, consisting of the lower part 62 and therotatable plate 61, has a slightly different setup to the one shown inFIG. 10: a plane disk which rotates together with the plate is appliedto the plate 61.

In a further difference to FIG. 10, an adapter plate 59 forming amechanical interface between the test body 1 and test object 2 isinstalled between the test body 1 and the part 66 of the rotary pivotjoint 2. As a mechanical interface, the adapter plate 59 enables the useof always the same test body 1 for a multiplicity of test objects.

FIG. 13 shows a measurement setup which is analogous to the setup inFIG. 12. In contrast to the setup of FIG. 12, the test object 201 inthis case is a rotary table, the rotational axis D of which is intendedto be calibrated or the rotational position error thereof, and furthermovement errors, are intended to be determined. The rotary table 201 isplaced onto a calibrated reference rotary table 60, the rotatable plateof which is rotatable about the rotational axis R. The reference rotarytable 60 has the same setup as in FIG. 12. The rotary table 201 has alower part 205 and a rotary plate 206 which is rotatable about the axisD. In contrast to FIG. 12, a different type of arm 78 for the sensorholder 72 is provided in the present setup.

An adapter plate 59 is placed onto the rotary plate 201. The test body 1is positioned on the adapter plate 59. The features of the test body 1were already explained on the basis of the preceding figures. The testbody 1 rotates together with the plate 206 of the rotary table 201 to becalibrated. The method for recording the rotational position error ofthe axis D is for example as follows:

-   (1) The plate 61 of the reference rotary table 60 is rotated about    an angle, e.g. +3° about the axis R. In the process, the lower part    205 of the test object rotary table 201 positioned on the plate is    likewise rotated by +3°. Following the rotation of the plate 61 of    the reference rotary table 60, or simultaneously therewith, the    plate 206 of the test object rotary table 201 is rotated about the    axis D in the opposite direction, for example by −3°. In the    process, the test body 1 is also rotated about the same angle, in    this example −3°. When observed from the inert system, the mirror 5    remains stationary as a result thereof. After completion of the    movement step, the position value of the mirror 5 is established by    the AKF 88. In the case of a rotational position error-free rotation    about the axis D, the position of the mirror 5 should be constant.    By contrast, a deviating position of the mirror emerges from a    rotational position error and the rotational position error is    determined using the AKF 88.

Further steps are analogous to the method described on the basis of FIG.10:

-   (2) Step (1) is repeated with different angle values, preferably    until a multiple of 360° is obtained. In the case of roller-borne    rotational axes, it is advantageous to acquire at least 2.5    rotations. Alternatively, the rotational movement and the angle    measurement with the AKF 88 can be implemented continuously.    Additional computational corrections can also be undertaken in order    to compensate for synchronization problems. The great advantage of    this method is that the increment can be selected to be very small,    i.e. even short-periodic error components are registrable in a    relatively short period of time.-   (3) Subsequently, the measurement of the remaining—in total    5—rotational and translational errors can occur. To this end, the    lower reference rotary table 60 is not rotated, i.e. the plate 61 is    fixed relative to the lower part 62 and only the test body 1 is    rotated together with the plate 206 about the axis D against the    lower part 205 of the rotary table 201.-   (4) Characteristic variables are calculated from the data obtained    and are compared to a given specification. Or correction values for    a CAA correction are established from the data.

The following examples describe further embodiments of a test body andthe peculiarities thereof:

FIG. 4 shows a test body 100 comprising a mirror 500 with the reflectionface 700 which faces away from the rotational axis D. Furthermore, thetest body has a second mirror 501 with a mirror face 701 which likewisefaces away from the rotational axis D. The two reflection faces 700 and701 are orthogonal to one another, wherein, in the selected view, themirror face 701 points in the direction of the observer and the mirrorface 700 is aligned laterally to the right in the direction of the AKF88. The lower part of FIG. 4 shows the setup from above with thedirection of view along the rotational axis D. In the lower part of FIG.4, a second AKF 81 which is aligned onto the mirror face 701 of thesecond mirror 501 is depicted.

Furthermore, the test body 100 of FIG. 4 also has a holder 300 and asphere 800 attached to the end of the holder. The mirrors are fastenedto the holder 300 with supports 600, 601. Alternatively, a cylinder, asshown in FIG. 3, or a double sphere, as in FIG. 2, can be providedinstead of a sphere 800. In contrast to the embodiment according to FIG.2, only one sphere is present; this is justified as follows: the doublesphere of FIG. 2 of the cylinder of FIG. 3 is only required forregistering the second tilt angle not registered by the AKF 88, in thiscase the tilt angle about the X-axis. If two mirrors 500, 501 and twoassociated AKFs 88, 81 are available, it is possible to dispense with adouble sphere or a cylinder as the second tilt angle can be registeredby the AKF 81 by way of the tilt of the mirror 501. As a result, it ispossible to dispense with two of the five distance sensors shown inFIGS. 12 and 12. The use of an AKF 81 is advantageous in that theworking distance can be larger and the apparatus can have a simplerconfiguration. The AKF offers the highest level of accuracy and areliable measurement.

FIG. 5 shows a test body 102 which has a mirror 502 that has areflection face 702 pointing in the direction of the rotational axis D.Expressed differently, the mirror face 702 points upward in theZ-direction. The mirror 502 is fastened to the sphere 800 by means ofthe support 602. All further elements were already described on thebasis of FIG. 4. Instead of a sphere 800, provision can alternatively bemade for a cylinder, as shown in FIG. 3, or a double sphere, as in FIG.1, wherein the mirror 502 would be fastened accordingly by means of thesupport 602 on the cylinder or the upper sphere of the double sphere. Asecond AKF 82 is directed to the mirror face 702 of the second mirror502 and measures the two tilts of the test body 102 about the X-axis andY-axis. Moreover, the axial sensor 77 shown in FIGS. 12 and 13 couldmeasure in the direction of the mirror 502 oriented in the axialdirection, or the reflection face 702 thereof, in order to determine thetranslation deviation in the Z-direction Tz.

FIG. 6: The embodiment of a test body 103 according to FIG. 6 is almostidentical to the embodiment according to FIG. 4, except for that thetest body 103 does not have a sphere 800 as rotationally symmetricalelement. In this embodiment, the translation in the X-direction isregistered by a distance sensor 741, which is depicted in the lower partof FIG. 6 (view of the setup in the −Z-direction). The translation inthe Y-direction is registered by a distance sensor 761 directed onto themirror 501. In this case, the determination of the three rotationalerrors (rotational position error of the axis D, Rx and Ry) and themeasurement of the translation errors Tx and Ty can be implementedsimultaneously. If the axial translation deviation Tz is likewiseintended to be registered, a counter face which points in theZ-direction can be attached to the test body 103. A further distancesensor can be directed to this counter face. By way of example,provision can be made for a third mirror 502, as depicted in FIG. 5,onto the mirror face 702 of which an AKF 82 and a further distancesensor are directed.

The goal of the arrangement from FIG. 6 is the simultaneous measurementof the position error (AKF 88, 81), a rotation (AKF 88, 81) and atranslation (distance sensor 741, 761) using the same mirror target 500or 501 in each case.

When using the arrangements of autocollimator (AKF)/distance sensor88/741 and 81/761, the distance sensor 741 or 761 is preferably arrangedfor the translation measurement in such a way that it is alignedcentrally on the mirror 500 or 501, to the extent that the mirrors 500and 501 themselves are also aligned centrally in relation to therotational axis D—expressed differently, to the extent that therotational axis D in the perspective of the upper FIG. 6 divides themirror 501 into two halves and the mirror 500 is correspondingly dividedinto two halves if it were to be viewed from the right. It would beadvantageous in this arrangement if the mirroring plane of the mirror500 or 501 were to be arranged in such a way that the rotational axis Dlies in this plane in order to avoid so-called cosine errors.

Expressed differently, the notional continuation of the measurement beamof the distance sensor 741 or 761 should impinge on the rotational axisD.

If the notional continuation of the measurement beam of the distancesensor 741 or 761 does not impinge on the rotational axis D, thefollowing points should be considered in practice: the drawn arrangementis therefore not preferred because the laser distance sensors 741 and761 are eccentric and a rotation of the mirror 500 or 501 as a result ofa position error would be interpreted by the laser 741 and 761 as atranslation due to the lever present. The changes in the distance causedby the rotation would add to the actual translations. The followingsolutions are feasible for this problem:

-   -   1. The distance sensor 741 or 761 is arranged in such a way that        the notionally extended beam of the laser intersects the        rotational axis, as already mentioned above. As a result, the        lever is dispensed with and the distance sensor 741 or 761 only        still sees the actual translation. It would be advantageous in        this arrangement if the mirroring plane of the mirror 500 or 501        were to be arranged in such a way that the rotational axis lies        in this plane. Otherwise so-called cosine errors are generated.        There are no problems with arranging the AKF eccentrically.    -   2. The distance change visible at the laser 741 or 761 due to        the rotation can be eliminated computationally. The rotational        angle is known as a result of the AKF measurement. The        relationship between the change in distance at the laser 741 or        761 and rotational angle can be determined by a simple rotation        of the reference rotary table with a stationary test object.        Here, the reference rotary table must additionally meet the        requirement of being as translation error-free as possible. The        translation determined by the laser 741 or 761 must be corrected        by the distance change caused by the rotation. Alternatively,        the relationship between rotational angle and distance change at        the laser can be calculated from the lever relationships.    -   3. The effect of the distance change caused by the rotation can        be averaged out if use is made of two lasers. What is important        for this is that one laser is arranged on the one side of the        rotational axis and the other one is arranged on the other side        of the rotational axis. That is to say, the signals must change        in antiphase. The two lasers are preferably arranged as exactly        as possible on one level and preferably have the same distance        from the rotational axis. However, the two distance measuring        units also be arranged as desired provided the distances between        the lasers and the rotational axis are known. Then, the lasers        can also both be arranged on one side of the rotational axis.

In place of a laser distance sensor 741 or 761, a capacitive distancesensor may also come into question since capacitive sensors can alsomeasure against metallically mirrored mirror surfaces.

FIG. 7 shows a test body 104 with a test element 1000 in a sphericalform, wherein the sphere 1000 is a first measurement body in accordancewith the general description of the invention. The test sphere 1000 isconnected to the holder 300 by way of a support 602. The holder has adouble sphere 800, 900, which was already described in the precedingembodiments and which is a second measurement body in accordance withthe general description of the invention, just like the cylinder 10(FIG. 3), the sphere 800 (FIG. 4) and double spheres 8, 9, shown in theother figures. In this embodiment, a CMM is used to measure the sphereposition of the sphere 1000 after the test body 104 was installed in aCMM, for example analogous to FIG. 12 or FIG. 13. In the shownembodiment, the center point P of the sphere 1000 serves as a referencepoint. The position of the reference point P can be determined in thevarious rotational positions of the test body 104 and the rotationalangle of the test body 104 can be determined from the positions of thereference point P and the distance of the reference point from therotational axis D. The rotational axis D need not necessarily extendthrough the holder 300 but can also extend next to it, as shown in FIG.11.

In an embodiment (not shown here), it is also possible to attach andmeasure a plurality of spheres 1000 on the test body 104. Using aplurality of spheres, it is possible to measure the movement error asdescribed in Busch, K.; Franke, M.; Schwenke, H.: Wiegand, U.:“Rückführung von Koordinatenmessgeräten durch Abschätzung der zuerwartenden Messabweichungen durch Simulation” Physikalisch-TechnischeBundesanstalt. 1996 research report. Or changes in rotational positioncan be established at a plurality of spheres. Using the example ofreflectors, a “flipping-over measurement” or multiple measurement wasdescribed in the general part of the description, with two mirrors whichare at an angle of >180° to 360° in relation to one another or withthree or more mirrors which are at an angle of >180° to <360° inrelation to one another, in particular at the angle=360°−[(N−2)/N]*180°(N is an integer 3) in relation to one another. A measurement with aplurality of spheres can also be implemented analogously, which spheresare arranged at a distance from the rotational axis and/or in a mannernot coaxial with the rotational axis, wherein a notional line from asphere to the rotational axis and a notional line from an adjacentsphere to the rotational axis are at an angle 360°/M in relation to oneanother, wherein M is an integer greater than or equal to 2, inparticular 2-8. In particular, each of the spheres has a referencepoint, in particular the sphere center point, and a notional line fromthe sphere center point of a sphere to the rotational axis and anotional line from the sphere center point of an adjacent sphere to therotational axis are at an angle of 360°/M in relation to one another.

The measurement accuracy of the CMM can be increased if the sphere 1000,as considered from the inert system, remains stationary, in an analogousmanner to what was explained above on the basis of a stationary mirrorin the case of counter-rotating reference rotary table plate and testbody. In the case of a stationary sphere, the measuring system of theCMM only needs to move around the sphere. Long travel paths of themeasuring system of the CMM are thus avoided. The rotational positionerror can be increased by a relatively large distance between the sphereand the axis D or a relatively long support 602.

FIG. 8 shows a test body 105 with a mirror 503, the reflection face 703of which is aligned in the rotational direction or counter to therotational direction, as depicted by a double-headed arrow. The mirror503 is connected to the holder 300 by way of a support 603. In theselected perspective, the view is onto the test body 105 along therotational axis. Alternatively, the mirror 503 can also be attached tothe pedestal 400 and connected directly to the holder 300 by thepedestal 400. In the case of a connection via the pedestal 400, themirror 503 can be placed onto the pedestal 400. In this embodiment, theAKF is replaced by a laser 79, which performs a distance measurement tothe surface 703 of the mirror 503. To this end, a laser beam 704 isdirected onto the surface 703. A change in the distance is measured whenthe mirror 703 rotates. The angle through which the test body 105 hasrotated is determined indirectly by way of the position of the mirror503 and emerges as=arctan(dx/r),where

-   dx=change in distance between the laser 79 and mirror face 703, and-   r=shortest distance of the laser beam from the rotational axis.

The test body 105 from FIG. 8 can also additionally have a cylinder, asphere or a double sphere.

FIG. 9 shows a test body 100 as is described on the basis of FIG. 4. Incontrast to the setup of FIG. 4, in the setup of FIG. 9, the position ofeach mirror 500, 501 is only measured using an AKF 88, the beam of whichis directed to the mirror 500 through a semi-transparent mirror and,simultaneously, also directed to the mirror 501 by reflection in thesemi-transparent mirror 200 and deflection in the mirrors 201 and 202.As a result of this arrangement, the rotational position error Rz isregistered by each one of the two mirrors 500, 501. Additionally, Ry isregistered in the first beam, i.e. on mirror 500, and Rx is registeredin the second beam, i.e. on mirror 501.

In variants of the above-described method, the registration of thevarious degrees of freedom can also be implemented in sequence. In thismanner it is possible, e.g., to initially observe a first mirror withthe AKF and then a second one in a further measurement procedure afterreconfiguration of the AKF.

In principle, a separate test body is feasible for each degree offreedom. Thus, for example, a mirror could be fastened relative to therotational axis first and a double sphere standard could be fastened ina second measurement procedure.

The subsequent FIGS. 14-23 show further arrangements comprising arotational device 201, in this case a rotary table, a referencerotational device 60, in this case a reference rotary table, andpossibly further components.

The setup of FIG. 14 is comparable to FIG. 1. The rotational device 201is arranged on a reference rotational device 60, wherein the stator 205of the rotational device 201 is connected in a conjointly rotatingmanner to the rotor 61 of the reference rotary table. A mirror 5 as atest element is attached to the rotor 206 of the rotational device 201,the rotational position of which mirror is registered by means of theautocollimator 88. An energy supply 802 in the form of a cable leads tothe stator 62 of the reference rotary table 60 and an energy supply 801in the form of a cable leads to the stator 205 of the rotary table 201.The cables 801, 802 also serve for signal transmission, e.g. of controland measurement signals to an error establishment unit 1001 depicted inFIG. 1. Within the meaning of the general description, the followingapplies in FIG. 14: the rotor 206 is the first part, the stator 205 isthe second part, the rotor 61 is the third part and the stator 62 is thefourth part. The arrangement could also be reversed, i.e. the referencerotary table 60 would then be arranged on the rotary table 201, whereinthe rotors would be arranged above the stator in each case. In thiscase, the sequence of the parts from top to bottom would be as follows:

-   -   reflector 5 on the rotor 62,    -   rotor 62 of the reference rotary table 60,    -   stator 61 of the reference rotary table 60, which undergoes        conjoint rotation with the rotor 205,    -   rotor 205 of the rotary table 201, which undergoes conjoint        rotation with the stator 61,    -   stator 206 of the rotary table 201.

In this arrangement, the stator 206 is the first part, the rotor 205 isthe second part, the stator 61 is the third part and the rotor 62 is thefourth part within the meaning of the general description. From thisassignment, it is obvious that the first part 206 in FIG. 14 is a rotor,whereas it is a stator in the above-described modification, where therotary table is arranged below, and that the second part 205 in FIG. 1is a stator, whereas it is a rotor in the development with reversedarrangement of rotational device 201 and reference rotational device206. Accordingly, the functions of the third and fourth parts 61, 62,which are part of the reference rotary table 60, are interchanged interms of the function thereof compared to FIG. 14 in the modification ofthe arrangement of FIG. 14. In FIG. 14, part 62 is a stator and part 61is a rotor, whereas, in the reversed arrangement of rotary table 201 andreference rotary table 60, part 61 is a stator and part 62 is a rotor.

In the subsequent description of the figures, the first part of thegeneral description is always assigned the reference sign 206, thesecond part is always assigned the reference sign 205, the third part isalways assigned the reference sign 61 and the fourth part is alwaysassigned the reference sign 62, independently of whether the relevantpart is a rotor or a stator in relation to the respective rotationaldevice or reference rotational device. In one definition, a stator of arotational device is the part which has an energy supply and a drive, bymeans of which the rotor is driven. If the rotational device is used asintended in measurement operation of a coordinate measuring machine, therotor is rotated while the stator remains stationary. Contrary to thisprinciple, the subsequent figures also describe arrangements which donot constitute the use of the rotational devices in the measurementoperation and in which the stator is rotated and the rotor remainsstationary, e.g. stationary in relation to a substrate.

A disadvantage of the setup from FIG. 14 is that the stator 205 of therotary table 201 is twisted in relation to the stator 62 of thereference rotary table 60 when the method is carried out and, as aresult thereof, the energy cables 801 and 802 are also twisted inrelation to one another, possibly leading to the winding of the cable801 in the case of a relatively large rotational angle or in the case ofmultiple rotations. The reflector 5 on the rotor 206 of the rotary table201 in FIG. 14 can be part of a test body described in the general partof the description, for example part of the test body 1 from FIG. 2 orof the test body 101 from FIG. 3 or of the test body 100 from FIG. 4 orof the test body 102 from FIG. 5 or of the test body 103 from FIG. 6,wherein the reference sign 500 should replace reference sign 5 when atest body in accordance with FIG. 4, 5 or 6 is used. Expresseddifferently, a test body which is conjointly rotating with the rotor 206and which has a reflector 5 or 500, to which a measurement beam isdirected using an autocollimator 88, can be positioned on the rotor 206.

FIG. 15 shows an arrangement in which the rotary table 201 was rotatedby 180° in comparison with FIG. 14. The rotor 205 of the rotary table201 is the second part in this case (by contrast, part 205 is a statorin FIG. 14) and the rotor 205 is connected in a conjointly rotatingmanner to the rotor 61 (third part) of the reference rotary table 60.The advantage over the setup of FIG. 14 is as follows: the method forestablishing an error of a rotational position establishment system ofthe rotary table 201, as described in this invention, can be performedin such a way that the stator 206 cannot be twisted in relation to thestator 62, or only by a little, and the problem of the winding of thecable 801 described in FIG. 14 is avoided. By contrast, the rotor 61 andthe rotor 205 coupled thereto in a conjointly rotating manner can berotated by any angle and in any direction relative to the stator 62 andrelative to the stator 206. As in FIG. 14, the setup of FIG. 15 can alsobe modified in such a way that the rotary table 201 is arranged at thebottom and the reference rotary table 60 is arranged at the top, whereinthe stators 62 and 206 are respectively arranged right at the bottom andright at the top, i.e. the overall setup of FIG. 15 could be rotated by180° such that it is upside-down, with the exception of the reflector 5which would then be arranged on the stator 62 of the reference rotarytable 60.

FIG. 16 shows a setup in which no rotational position establishmentapparatus 88, i.e., in particular, no autocollimator 88, is required forperforming a method for establishing an error of the rotational positionestablishment system of the rotary table 201. The meaning of the parts61, 62, 205, 206 is the same as in FIG. 15. In this embodiment, thestator 206 of the rotary table 201 is connected to a substrate 304 in aconjointly rotating manner by way of a support 302. The stator 62 of thereference rotary table 60 is also arranged on the substrate 304 in aconjointly rotating manner such that, overall, the stators 62 and 206undergo conjoint rotation. The rotors 61, 205 are connected to oneanother by means of a rotationally rigid coupling 303 and the rotors 61,205 can be twisted synchronously in relation to their respectivestators. Here, it is sufficient if one of the rotors 61 or 205 is drivenand the respective other rotor is driven by way of the rotationallyrigid coupling 303. The arrangement of FIG. 16 is suitable forperforming variant e) of the method for the error establishmentdescribed in the general part of the description. In this variant, theresultant rotational positions of the first part 206 and of the fourthpart 62 are not changed, i.e. part 206 is not rotated relative to part62. In this case, it is not necessary to determine the unchangedrotational position of the first part 206 and of the fourth part 62relative to one another by means of an external establishment apparatus88 as the two parts 62 and 206 are rotated conjointly in relation to oneanother as a result of a mechanical connection by way of the support302. By way of example, the rotationally rigid coupling 303 can be abellows coupling, a claw coupling or a (double) Cardan-type joint. Ifone rotary table drives the other, as mentioned above, tension isavoided. Like in FIG. 15, the rotary table 201 could also be arranged atthe bottom in FIG. 16 and the reference rotary table 60 could bearranged at the top, wherein, once again, the two stators 62 and 206would be connected in a conjointly rotating manner to one another by wayof the support 302 and the substrate 304. In this variant, the stator 62of the reference rotary table 60 would be attached to the support 302and the stator 206 of the rotary table 201 would be positioned on thesubstrate 304. In FIG. 16 and the variant just described, the two rotorsare connected in a conjointly rotating manner by way of the coupling303. There likewise are the two variants in which the two stators areconnected in a conjointly rotating manner to one another by way of thecoupling 303 and the rotors are connected in a conjointly rotatingmanner to one another by way of the support 302 and the substrate 304,wherein the disadvantages of the cable guide occur due to co-rotatingcables.

In FIG. 17, the stator 61 of a reference rotary table is placed on apedestal 305, which in turn is placed on a substrate 304. The stator 61is the third part within the meaning of the general description. Anautocollimator 88 is positioned on the rotor 62 of the reference rotarytable 60 (fourth part within the meaning of the general description).The measurement beam S of the autocollimator 88 is directed to a mirror5 which is fastened to a rotor 206 of a rotary table 201. The rotor 206is the first part within the meaning of the general description. Thestator 205 (second part within the meaning of the general description)is attached to a support 302 which is connected to the substrate 304.The resultant rotational position of the first part 206 and of thefourth part 62, which are both rotors in this example, is determinedwith the aid of the autocollimator 88. It is likewise possible to usethe AKF 88 to establish a change in the rotational position of the rotor206 relative to the rotor 62 after varying the rotational positions ofthe rotary table 201 and of the reference rotary table 60, or anunchanged position of the parts 62 and 206 relative to one another canbe determined using the ATF 88. Variations are also feasible in thesetup of FIG. 17. By way of example, the ATF 88 could be attached to therotor 206 and the mirror 5 could be attached to the rotor 62. Also, thereference rotary table 60 could be positioned at the top and the rotarytable 201 could be positioned at the bottom, wherein the stator 61 ofthe reference rotary table 60 would then be fastened to the support 302and the stator 205 of the rotary table 201 would be fastened to thepedestal 305 or to the substrate 304. In further variants, rotor andstator could be interchanged, i.e. parts 62 and 206 could respectivelybe a stator, wherein disadvantages of the cable guide occur due toco-rotating cables.

The rotational direction of a rotary table can be defined within arotary table-inherent coordinate system in such a way that, in the caseof a suspended rotary table, as shown by reference sign 201 in FIGS. 16and 17, the positive rotational axis direction points downward and, inthe case of a standing rotary table, as shown by reference sign 60 inFIGS. 16 and 17, it points upward.

FIG. 18 constitutes a variant of the setup from FIG. 15. In this case,the ATF 88 is positioned on the rotor 206 of the rotary table 201 andcan therefore co-rotate with the rotor 206. The mirror 5 is fastened onthe substrate 304 in a manner stationary in relation to the stator 62 ofthe reference rotary table 60. By way of example, the setup of FIG. 15can be modified in this manner: the ATF 88 can be attached to the part206 and the reflector 5 can be attached to the substrate 304.

FIG. 19 constitutes a variant of the arrangement from FIG. 16. In thiscase, the rotationally rigid coupling 303 is positioned between thesupport 302 and the stator 206 (the first part within the meaning of thegeneral description in this case). Like in the setup from FIG. 16, norotational position establishment apparatus, i.e., in particular, no ATF88, is required in the setup in relation to FIG. 19.

FIG. 20 shows an embodiment where the rotational axis D of a rotationaldevice 201 and the reference rotational axis R of a reference rotationaldevice 60 are not coaxial or not flush with one another, but ratherarranged next to one another. A reference rotary table 60 is positionedon the substrate 304 with a stator 61 (third part within the meaning ofthe general description) and a rotary table 201 is positioned on thesubstrate 304 with the stator 205 (second part within the meaning of thegeneral description) thereof. The two stators 61 and 205 rotate in aconjoint manner in relation to one another. An autocollimator 88 ispositioned on the rotor (rotary plate) of the reference rotary table 60.The rotor 62 is the fourth part within the meaning of the generaldescription. A mirror 5, onto which the measurement beam S of theautocollimator is directed, is positioned on the rotor (rotary plate)206 of the rotary table 201. The rotor 206 is the first part within themeaning of the general description.

FIG. 20b shows a plan view of the arrangement from FIG. 20a , whereinthe rotary table 201 and the reference rotary table 60 are situated in afirst rotational position. FIG. 20c likewise shows a plan view of thearrangement, wherein the reference rotary table 60 and the rotary table201 were brought into a second rotational position compared to FIG. 20b. Both rotary plates (in general: rotors) 62 and 206 were rotated in thesame direction, in this case counterclockwise in the plan view. In thisarrangement, a measurement over a restricted angular range is possibleuntil the measurement beam S is no longer incident on the mirror 5.Using the autocollimator 88, it is possible to register a differentrotational angle of the rotary plate 206 compared to the rotationalangle of the rotary plate 62, or it is possible to determine that bothplates or rotors 62 and 206 were twisted by the same angle. In themethod for establishing one or more errors of a rotational positionestablishment system, which is described in the general description,this corresponds to method variants d) and e). In a development of thearrangement of FIG. 20, rotor and stator could be interchanged in therotary table 201 and/or in the reference rotary table 60, i.e. one orboth of the rotary plates 62 and 206 could be positioned on thesubstrate.

FIG. 21 shows an arrangement of a reference rotary table 60 and a rotarytable 201, like in FIG. 20. In this case, a prism with a pentagon-shapedbase area, the side faces of which are mirrored, is used instead of asingle plane mirror 5. Thus, overall, 5 reflectors 5 a, 5 b, 5 c, 5 d, 5e are present which are applied to the side faces of the pentagon-shapedprism and are at an angle of=360°−[(N−2)/N]*180° with N=5, i.e. at an angle of=360°−[(5−2)/5]*180°=360°−108°=252°in relation to one another. The angle plotted in FIG. 21 specifies theinternal angle of the pentagon, which is [(5−2)/5]*180°=108°. In thearrangement of FIG. 21, a rotation of the rotary plate 206 about largerangles in comparison with FIG. 20 is possible. In principle, there canbe full rotations about 360° of the rotary table 206. As soon as one ofthe mirrors or one of the mirrored side faces of the prism, e.g. themirror face 5 a, leaves the measurement beam S of the autocollimator,the next adjacent mirror face—the mirror face 5 b in the case of acounterclockwise rotation—is rotated into the measurement beam S of theautocollimator and the measurement can be continued, as shown in FIG. 21b.

Using the arrangement of FIG. 21, it is also possible to carry out amethod in which the method with steps a) to d) and/or e) according tothe general part of the description is performed, wherein, when thismethod is carried out, the measurement beam of the autocollimator 88 isdirected to one of the mirror faces, e.g. 5 a. The AKF on the rotor 62can be displaced in such a way that the measurement beam points 180° inthe opposite direction and, subsequently, the rotor 62 can be rotated by180° such that the beam S is once again, like previously, incident onthe mirror face.

Subsequently, method steps d) and/or e), which are described in thegeneral part of the description, can be carried out anew. This methodcan be combined with a rotation of the rotary plate 206 and themeasurement of further mirror faces, as described above. This procedureis referred to as a flipping-over measurement, deviating from theprocedure otherwise referred to as flipping-over measurement, which isonly referred to as “flipping-over” following a rotation about 180°.

In two different views—once from the side in FIG. 22a and once fromabove in FIG. 22b —FIG. 22 shows a setup analogous to FIG. 14, wherein,in contrast to FIG. 14, a rotary angle is not measured by anautocollimator 88 but by using two distance sensors 306 and 307, themeasurement beams S1 and S2 of which are directed to the reflector 5. Byusing two sensors 306 and 307, which are arranged next to one anotherand preferably arranged level with one another and preferably arrangedat the same distance from the reflector 5, it is possible to distinguishbetween translation movements of the reflector 5 and rotation movementsof the reflector 5 since, in the case of a rotation of the reflector 5,the distance to one of the sensors is reduced and the distance to therespective other sensor is increased.

FIG. 23 shows a setup analogous to FIG. 17, where no AKF 88 whichco-rotates with the rotor 62 is provided. Rather, provision is madeeither for an AKF 88 or an AKF 881, which are both plotted but usedalternatively. The measurement beam S1 of the AKF 88 is incident on themirror 309 and is deflected by the mirror 309 through the concentricpassage bore 308 onto the mirror 310, and from there to the mirror 5. Ifthe AKF 881 is used instead of the AKF 88, the mirror 309 is dispensedwith and the measurement beam S2 of the AKF 881 passes directly throughthe concentric passage bore 308 and is deflected to the mirror 5 by themirror 310. The measurement with two AKFs 88 and 881 would also beconceivable, wherein the mirror 309 would then have to have asemi-transparent embodiment. The measurement accuracy could be increasedby using two AKFs 88 and 881.

FIG. 24 elucidates the principle of a flipping-over measurement whichwas already mentioned in the general part of the description. In orderto compensate for residual errors of the angle calibration type, thebasic method for establishing the error of a rotational positionestablishment system, with steps a) to e) and as described in thegeneral description, can be applied using the test body described hereinwith a plurality of reflector layers, which are preferably distributeduniformly, and by using multiple measurements in a so-calledflipping-over measurement. Causes for possible residual errors can liein the type of setup, the arrangement of the employed components and/orsystematic residual errors of the measuring system of the referencerotational device 60, or lie in further sources of error.

In FIG. 24, a setup analogous to FIG. 14 is used, wherein use is made ofa test body 106 which has two reflectors 5 a and 5 b as first and secondtest elements. The reflectors 5 a and 5 b point in opposite spatialdirections, i.e. in directions that are at 180° to one another.

Here, the flipping-over measurement can be performed as follows:

-   -   In a first measurement, shown in two different views (from the        side and from above) in FIG. 24a and FIG. 24b , the rotary table        201 is set to a start position (first rotational position), for        example the reference marker or zero marker of the rotational        position establishment system of the rotary table 201. In FIG.        24a , the start position is symbolically depicted on the stator        205 and on the rotor 206 by two wedge-shaped markings. The        reference rotary table 60 is positioned in such a way that it is        possible to measure in the direction of the mirror 5 a using the        AKF 88, i.e. the measurement beam S is incident on the mirror 5        a and then returns or is reflected back to the AKF.    -   The rotational position of the reference table 60 is likewise        set to a start position (first rotational position), for example        the reference marker or zero marker of the rotational position        establishment system of the reference rotary table 60. In FIG.        24a , the start position is symbolically depicted on the stator        62 and on the rotor 61 by two line-shaped markings.    -   Now the actual measurement, in which the rotor 206 of the        rotational device 201 and the rotor 61 of the reference        rotational device 60 are rotated in different directions in        relation to one another, depicted by arrows in FIG. 24b , is        implemented. Using the AKF 88, the rotational position error of        the rotational position establishment system of the rotary table        201 is established. To this end, reference is made to the        description of steps d) and e) of the method for establishing        the error of the rotational position establishment system.    -   For a second measurement, which is shown in FIG. 24c and FIG.        24d , a modified first rotational position is established as        follows in the reference rotary table: the rotor 61 is twisted        by 180° (360°/M with M=2) compared to the position shown in FIG.        24b . In this modified first rotational position, it is once        again possible to set a reference marker or zero marker of the        rotational position establishment system of the reference rotary        table 60 (in the controller of the rotary table 60) as a start        point for the measurement, or the newly set angle of 180° of the        reference rotary table is noted as the offset angle of the        reference rotary table and taken into account. Starting from        this start point, when once again establishing the error of the        rotational position establishment system, the rotor 61 of the        reference rotary table 60 can be rotated about a whole rotation        of 360°, for example from 180° to 540° or from −180° to 180° in        the case of a 180° offset and in the case of a positive rotation        of the reference rotary table—if the reference rotary table        rotates in the negative direction, the rotation occurs e.g. from        180° to −180° or from −180° to −540°.    -   The whole rotary table 201 was rotated together with the rotor        61 such that now—as depicted in FIG. 24 c/d—the measurement beam        S of the AKF 88 is incident on the mirror 5 b instead of on the        mirror 5 a. The start position or first rotational position of        the rotary table 201, i.e. the position of the rotor 206 in        relation to the stator 205, is unchanged, as is visible in FIG.        24d on the basis of the symbolic wedge-shaped markings (in FIG.        24c , these lie covered on the rear side).    -   A modified rotational position of the first part 206 and of the        fourth part 62 relative to one another is obtained as a result        of the modified first rotational position of the reference        rotary table 60. In this case, the fourth part is twisted        relative to the first part by an angle value of 360°/2 compared        to the first resultant rotational position of the first part 206        and of the fourth part 62 relative to one another, which is        shown in FIG. 24 a/b.    -   Proceeding from the rotational position shown in FIG. 24 c/d,        the error of the rotational position establishment system of the        rotary table 201 can be established anew, wherein reference is        made to the description of steps d) and e) of the method for        establishing the error of the rotational position establishment        system.    -   The measurement using the setup according to FIG. 24a /24 b is        referred to as “measurement 1” and the new measurement        proceeding from the setup of FIG. 24c /24 d is referred to as        “measurement 2”. After implemented measurements 1 and 2, the        measured angle position errors of the rotary table 201 from        measurements 1 and 2 are combined in a suitable manner by        calculation, wherein the forming of an average taking into        account the rotary angle of the rotational device 201 is        preferred. Other ways of combining the individual measurements        by calculation are feasible.

This method can be performed with any number of mirror faces, forexample with five mirror faces, as shown in FIG. 21. By way of example,use can be made of N mirror faces, which are preferably at an angle of=360°−[(N−2)/N]*180° in relation to one another, where N is an integergreater than or equal to 3. In principle, the following applies here:the greater the number of measurements is, the more error components canbe eliminated by this principle of the multiple measurement. Using twomeasurements, it is possible to eliminate errors due to theaforementioned causes, which would be noticeable in the first errorharmonics (these are also referred to as first order errors). Using fourmeasurements, the first and the second errors harmonics are eliminated;using six measurements, the first to the third error harmonics inclusiveare eliminated, etc. For four measurements, use can be made of e.g. atest body with a prism with a square base area (which can also bereferred to as cube or cuboid), wherein the side faces of the prism aremirrored. For five measurements, use can be made of a prism with apentagon-shaped base area, the side faces of which are mirrored. For sixmeasurements, use can be made of a prism with a hexagon-shaped basearea, the side faces of which are mirrored, etc.

The results of the exemplary flipping-over measurement for the mirrors 5a and 5 b in accordance with FIG. 24 are depicted in FIGS. 25 and 26. Inthe measured error signal in FIG. 25, only the first error harmonic wascontained and it could be eliminated apart from residual noise. Theresidual noise is the sought-after position error without the residualerrors of the setup. In FIG. 26, the second error harmonic wasadditionally contained and this could not be eliminated in the case ofthe flipping-over measurement using two measurements.

FIG. 27 shows a holding element, in which the support has a third limb511 in addition to the first limb 51 and the second limb 52. The thirdlimb 511 has a coupling region 92, which is referred to as a thirdcoupling region and by means of which the holding element 510 iscoupleable to the base 61. In this case, a plane disk 790 is attached tothe rotor 61 of the reference rotary table 60, on which plane disk theholding element 510 with the third coupling element 92 has been placed.The third coupling region 92 has coupling means 512, 513 and 514, whichare analogous to the coupling means 55, 56 and 58 of the first couplingregion 90 and to the coupling means 53, 54 and 57 of the second couplingregion 91. These coupling means were already explained on the basis ofFIG. 10. In this exemplary embodiment, the coupling means 512 and 513are spherical elements, wherein, in the selected perspective, theelement 513 is covered by the element 512 lying at the front. Togetherwith a knurled screw 514, the sphere-shaped elements 512 and 513 form athree-point bearing. The spheres 512 and 513 can, together with thebearing point in the screw 514, lie on the corners of a notionalequilateral or isosceles triangle, with this not being mandatory.Likewise, the coupling means 55, 56, 58 or the coupling means 53, 54, 57can lie on the corners of an equilateral or isosceles triangle.Together, the limbs 51, 52 and 511 from a C-shaped support. Thisembodiment is particularly advantageous for CAA data recording of theshown A-axis of a rotary pivot joint 2 in the subsequent installationposition thereof. The position of the rotary pivot joint 2 shown in FIG.27 corresponds to the subsequent installation position during themeasurement operation, for example on a sleeve of a coordinate measuringmachine. A method for recording the rotational position error of axis Bwas described on the basis of FIG. 10; this can also be performedanalogously for the A-axis. In this method, the C-shaped support rotatestogether with the rotor or rotary plate of the reference rotary table 60about the rotational axis R of the reference rotary table 60. The part66 is rotated about the axis A in the opposite rotational direction ifthe rotation about R and about A is observed along the axes from thesame direction of view, for example from above.

In the case of a rotation, the terms “co-rotating” or “same direction”and “counter rotating” or “opposite direction” generally assume the sameobservation position, i.e. the same observation position of an externalstationary observer, wherein the observation position of the externalstationary observer is also referred to as “inert system”. Therotational movement of the holding element 510 leads to the limb 52being moved into the measurement beam S of the AKF 88 and covering themeasurement beam in the case of a solid limb 52 such that saidmeasurement beam is no longer incident on the mirror 5. By way ofexample, the following solutions exist for this problem:

-   -   The perpendicular limb 52 contains a perforation 515, which is        depicted in FIG. 27 by two horizontal dashed lines. As a result,        the width of the shadowing of the beam S is reduced. The sealed        regions could remain unconsidered and be interpolated in a CAA        correction field.    -   The shadowed regions could therefore lie between the support        positions in the case of a large support position width, i.e. in        the case of a large distance between the angle positions driven        to during the method.    -   The perpendicular struts, i.e. the regions of the limb 52, which        lie between the edge of the recess 515 and the lateral outer        edge of the limb 52, could be embodied to be so narrow that the        aperture of the AKF 88 is not completely covered, and so        measurements can nevertheless be performed. This is conceivable,        in particular, if a tripod is used instead of a C-shaped        support, in which the perpendicular supports can be narrow.    -   In the method, it is not always necessary to perform full        rotations of the rotor 61, i.e. it is not always necessary to        measure 360°. Moreover, the rotary pivot joint 2 can have a        rotational range about the axis A which cannot be approached and        in which the limb 52 could be arranged.    -   The method could be performed using two AKFs, which observe the        rotary pivot joint 2 from two different directions.    -   The beam S could be deflected by deflection mirrors onto the        mirror 5, i.e. it could be guided past the limb 52 which        interrupts the straight-line path of the measurement beam S.

The above-described problem of the measurement beam S being covered canoccur not only in the C-shaped support from FIG. 27 but also indifferent types of support which could cover the measurement beam S whenthey are rotated accordingly. By way of example, the limb 51 in FIG. 10could interrupt the measurement beam S, which is incident on the mirror5 coming from the AKF 88, in the case of a corresponding rotation of theholding element 50 about the axis R. One or more of the above solutionscould also be applied in this embodiment of FIG. 10. In very generalterms and detached from the specific exemplary embodiment, the supportof a holding element according to the invention can have one or moreperforations for a measurement beam. One or more perforations canrespectively be provided in one of more of the coupling regions.However, the geometry and dimensions of the limbs could otherwise alsobe selected in such a way that no interruption of the beam occurs.

In another arrangement of the holding element 510 on the rotor 61 of thereference rotary table 60, the B-axis can be measured according to ananalogous method as for the A-axis. To this end, the holding element 510can be placed onto the surface of the plane disk 790 by means of thecoupling region 91; i.e. it can be rotated 90° counterclockwise in thedepicted perspective. Subsequently, the mirror 5 is reoriented in such away that the measurement beam S of the AKF 88 is incident thereon in thesame way as shown in FIG. 27. As depicted in FIG. 27, the mirror 5 couldthus be covered either by the limb 51 or by the limb 511, depending onthe rotational position of the holding element 510. In order to avoidthis, it is possible either to apply one of the solutions proposedabove, e.g. respectively provide a perforation in the limb 51 and in thelimb 511 (not depicted here) or the mirror 5 can be positioned so fartoward the top together with the AKF 88 that it projects beyond thelimbs 51 and 511. To this end, use can be made of e.g. a test body, asshown e.g. in FIG. 10 by means of the reference sign 1, where the mirror5 is attached at a fitting level to a holder 3.

FIGS. 28 and 29 show elements of an alternative apparatus for supplyingenergy to the rotational device 2. An energy supply 69, as shown inFIGS. 10 and 11, can be replaced by these elements 690 and 691. The part690 or 690′ from FIG. 28 is combinable with the part 691 or 691′ fromFIG. 29 so as to form a plug-in or latching connection. By way ofexample, an element 690 can be provided in one or more of theabove-described coupling regions 90, 91 or 92 (see FIG. 11 and FIG. 27of a holding element 50 or 510). Preferably, respectively one element690 is provided in each one of the coupling regions 90, 91 and 92. Byway of example, a first plug-in element 690 is arranged on the outerside of the limb 51, i.e. on the side of the limb 51, which faces thebase 61. Hence, the plug-in element 690 is situated in the couplingregion 90. When using the element 690 in a coupling region 90, it ispossible to dispense with the coupling means 55, 56 and 58 since thecoupling means 55, 56 and 58 are replaced by the means 692, 693 and 694.The analogous principle can be applied to other limbs/in differentcoupling regions.

In this example, a second element 691 is arranged at the base and shownin FIG. 29. When the holding element 50 is placed onto the base 61, theelements 690 and 691 are connected to one another. The element 690 for aplug-connection has bearing means 692, 693, 694 (694 is covered by thecentrally raised male connector part). The bearing means have a formshaped like a hemisphere. The bearing means 692, 693, 694 can be meansof a three-point bearing, which can be used as an alternative to theabove-described coupling means 55, 56, 58. Moreover, clamping/latchingmeans 695, 696 in the form of hemispheres are provided for a bayonetclosure. A further, third latching means is covered in this view. Theplug-in connection element 690 has a multiplicity of contacts 697 fortransmitting energy and measurement system signals. A metal plate 698 isprovided for interacting with a magnet 917 which is provided on theother complementary connector part 691 in order to exert a pullingforce. As a result, contacting can be ensured in addition to the bayonetclosure. The plug-in element 690 shown in FIG. 28 can also be providedin an analogous fashion to the rotational device 2 and is denoted by thereference sign 690′ in this case for distinguishing purposes. If anelement 690′ is provided at the rotational device 2, then the holder 68(see FIG. 11) for the rotational device 2 has a plug-in connectionelement 691′, as shown in FIG. 29. The holder 68 can itself be embodiedas plug-in connection element 691′.

FIG. 29 shows the already mentioned plug-in connection element 691 or691′ which is provided at the base 61 and/or at the holding element 50on the side of a holder 68. The plug-in connection part 691/691′ hascounter bearing means 910, 911, 912, which are embodied as hemispherepairs. The counter bearing means 910, 911, 912 serve to receive thebearing means 692, 693 and 694 from FIG. 28. Furthermore, a bayonet withthe recesses 913, 914 and 915 is present, into which the elements 695,696 and the further element (not shown) from FIG. 28 are insertable. Amultiplicity of counter contacts 916 are connectable to the contacts 697from FIG. 28 for establishing the contacting. A magnet 917, whichinteracts with the metal plate 698 from FIG. 28, is provided in thecenter of the plug-in connection element 691.

A plug-in connection made of parts 690 and 691 can also be used toinclude other components, which require an energy supply, into ameasurement setup. By way of example, an AKF 88 can be connected to arotatable part of a rotational device by means of such a plug-inconnection, for example if an AKF is intended to be connected to a rotor62 or 206, as depicted in FIGS. 17 and 18.

FIGS. 31 and 32 show the use of a holding element 520 for holding asensor arrangement 750 which has a plurality of sensors 73, 74, 75, 76,77, wherein the sensors are configured to measure deviations in respectof at least one degree of freedom of movement of the rotational device2. The rotational device is a rotary pivot joint 2 with two rotationalaxes A, B. Such a rotary pivot joint 2 was already explained in FIGS.10-12. However, in this example the rotary pivot joint 2 is not attachedto the holding element 520, as is the case in FIGS. 10-12, but rather toa perpendicular sleeve 590 of a coordinate measuring machine notdepicted in any more detail. Here, the rotary pivot joint 2 is situatedin its installed position for future measurements.

In terms of the setup thereof, the sensor arrangement 750 in FIGS. 31and 32 was already described in FIGS. 12 and 13. The arrangement has asensor holder 72 and sensors 73, 74, 75, 76, 77. The sensors 73, 74, 75,76, 77 are attached to the sensor holder 72, which has three walls whichare perpendicular to one another. In a first spatial direction, thesensors 73, 74 point to the spheres 8 and 9 of a test body 107 (notaccording to the invention); the sensors 75, 76 point to the spheres 8and 9 of the test body 107 in a second spatial direction. In theselected perspective of FIGS. 30 and 31, the sensors 75, 76 are behindthe spheres 8, 9 and therefore drawn with dashed lines. The sensor 77points to the sphere 9 in a third spatial direction. The spatialdirections can be the axes of a Cartesian coordinate system, wherein theassignment to one of the axes X, Y and Z depends on the location of thecoordinate system and the current orientation of the holding element 520and the sensor arrangement 750 connected therewith.

In contrast to FIG. 12, the sensor arrangement 750 is attached to theholding element 520 in FIGS. 30 and 31 by virtue of the sensor holder 72being connected to the holder 68. Apparatuses for the energy or datatransmission from or to the sensors 73, 74, 75, 76, 77 and an evaluationunit are not depicted in FIGS. 30 and 31.

Like the holding element 50 in FIGS. 10-12, the holding element 520 alsohas two limbs 51 and 52. The coupling regions 901 and 902 have aslightly different design to the coupling regions 90 and 91 in FIGS.10-12. In FIGS. 10-12, the bearing elements 53, 54, 55, 56 have ahemispherical form, wherein this can in each case be a hemisphere orelse a whole sphere which is partly sunk into the limb. The bearingelements 530, 540, 570, 550, 560, 580 have the form of a whole sphere inFIGS. 30 and 31, but that makes no difference to the functioningthereof. Fastening means for fastening the bearing elements 530, 540 and550, 560, 580 to the limbs are not shown.

The bearing elements 530, 540 and 570 are attached to the limb 52 andform a three-point bearing, wherein only the front element 530 of thebearing elements 530, 540 is visible in the selected perspective. Thespherical bearing element 570 is attached to the end of a set screw 585.One or both of the bearing elements 530 and 540 can also be attached tothe end of a set screw. Other adjustment possibilities are alsopossible. In an analogous manner to the limb 52 there are the bearingelements 550, 560 and 580 are attached to the limb 52 and form athree-point bearing, wherein only the front element 550 of the bearingelements 550, 560 is visible in the selected perspective. The sphericalbearing element 580 is attached to the end of a set screw 586. One orboth of the bearing elements 550 and 560 can also be attached to the endof a set screw.

In FIG. 30, the holding element 520 is coupled to the base 611 by thecoupling region 901. The coupling is implemented by way of countercoupling means 612, 613 (covered by 612 in this illustration) and 614,which are attached to the base and interact with the spherical bearingelements 530, 540 and 570. Further counter coupling means can be presenton the base in order to establish a different position of the holdingelement 520. In this example, the base 611 is not the reference rotarytable 60 as in FIG. 12, but rather a base, in particular a measuringtable, of a CMM. In FIG. 31, the same holding element 520 is coupled tothe base 611 in an analogous manner as in FIG. 30, but it is coupled viathe coupling region 902 unlike via 901 as in FIG. 30. The coupling inFIG. 31 is likewise implemented by way of the counter coupling means612, 613 and 614. In FIGS. 30 and 31, dimensions of parts sometimesdeviate from one another in the drawn representation, without this beingthe case in reality. By way of example, the holder 3 is drawn to beshorter in FIG. 31 than in FIG. 30, which is indicated by interruptionsin the form of double lines.

As shown in FIGS. 30 and 31, the sensor arrangement 750 can be orientedin such a way that the rotary pivot joint 2, to which the test body 107is attached with the double sphere 8, 9, can be qualified in theinstalled position thereof. The position of the rotary pivot joint 2remains unchanged in FIGS. 30 and 31 and corresponds to the installedposition for measurements. Only the arrangement of the test body at therotary pivot joint 2 is modified and aligned in a manner coaxial eitherto the A-axis (FIG. 31) or the B-axis (FIG. 30). The alternative ways offastening a test body to a rotary pivot joint are already shown in FIGS.10 and 11 in an analogous manner. In FIG. 31, the fastening isimplemented with the aid of an adapter 65 which is fastened magneticallyto the rotary pivot joint 2. After reorienting the test body 107, thesensor arrangement 750 with the holding element 520 is also oriented ina fitting manner to the test body 107 such that the sensors 73, 74, 75,76, 77 are aligned toward the spheres 8 and 9 in a fitting manner.Recording of movement errors can be implemented when the test body isrotated about the A-axis or the B-axis.

The invention claimed is:
 1. A method for: establishing one or more errors of a rotational position establishment system that measures rotational positions of parts of a rotational device; and/or establishing a hysteresis effect in the rotational position establishment system, the rotational device including a first part and a second part rotatable relative to one another about a rotational axis of the rotational device, the method comprising the steps of: establishing a first rotational position of the rotational device with first and second parts rotatable relative to one another, wherein a first rotational position of the first part is established relative to the second part of the rotational device; establishing a first rotational position of a reference rotational device, which is a rotary table including a third part and a fourth part rotatable relative to one another, wherein the third part, in relation to the rotational axis, is coupled in a conjointly rotating manner to the second part of the rotational device, and the fourth part is rotatable relative to the third part about a rotational axis of the reference rotational device, wherein a first rotational position of the third part is established relative to the fourth part; wherein a first resultant rotational position of the first part and of the fourth part relative to one another in relation to at least one of the rotational axis of the rotational device and the rotational axis of the reference rotational device results from the first rotational position of the rotational device and the first rotational position of the reference rotational device; varying the rotational position of the rotational device to a second rotational position of the rotational device and establishing the second rotational position of the rotational device using the rotational position establishment system; varying the rotational position of the reference rotational device to a second rotational position of the reference rotational device and establishing the second rotational position of the reference rotational device; wherein the first part is rotated against the second part in one direction, and the third part is rotated against the fourth part in a direction opposite to the one direction when varying the rotational positions of the rotational device and the reference rotational device; establishing a resultant rotational position of the first part and of the fourth part relative to one another, which resultant rotational position has been changed as a result of varying the rotational positions in the varying steps; establishing the rotational position error of the rotational position establishment system from the changed resultant rotational position of the first part and of the fourth part relative to one another; restoring the position of the rotational device to the first rotational position of the rotational device or substantially to the first rotational position of the rotational device and producing a modified first rotational position of the reference rotational device when the first rotational position or substantially the first rotational position of the rotational device is restored; or restoring the position of the reference rotational device to the first rotational position of the reference rotational device or substantially to the first rotational position of the reference rotational device and producing a modified first rotational position of the rotational device when the first rotational position or substantially the first rotational position of the reference rotational device is restored; such that, in the modified first rotational position of the rotational device or the modified first rotational position of the reference rotational device, there is a modified rotational position of the first part and of the fourth part relative to one another, wherein the fourth part is twisted relative to the first part by an angle value compared to the first resultant rotational position of the first part and of the fourth part relative to one another; with the first or substantially the first rotational position of the rotational device and the modified first rotational position of the reference rotational device, or with the first or substantially the first rotational position of the reference rotational device and the modified first rotational position of the rotational device: varying the rotational position of the rotational device to a further rotational position of the rotational device and establishing the further rotational position of the rotational device using the rotational position establishment system; varying the rotational position of the reference rotational device to a further rotational position of the reference rotational device and establishing the further rotational position of the reference rotational device; establishing a resultant rotational position of the first part and of the fourth part relative to one another, which resultant rotational position has been changed as a result of varying the rotational positions in the varying steps; and establishing the rotational position error of the rotational position establishment system from the changed resultant rotational position of the first part and of the fourth part relative to one another.
 2. The method as claimed in claim 1, in which the changed resultant rotational positions of the first part and of the fourth part relative to one another are established with the aid of a rotational position establishment apparatus.
 3. The method as claimed in claim 2, in which the rotational position establishment apparatus is one or more of an autocollimator, a tactile measuring head system of a coordinate measuring machine, an optical sensor of a coordinate measuring machine, a laser interferometer and a distance sensor.
 4. The method as claimed in claim 2, in which the changed resultant rotational position of the first part and of the fourth part relative to one another is established with the aid of a test element, and the rotational position or change in rotational position of the test element relative to the rotational position establishment apparatus is established by means of the rotational position establishment apparatus.
 5. The method as claimed in claim 4, wherein: the rotational position establishment apparatus is positioned in a conjointly rotating manner in relation to one of the first part and the fourth part; the test element is positioned in a conjointly rotating manner in relation to one of the first part and the fourth part; wherein the rotational position establishment apparatus is conjointly rotating in relation to the first part if the test element is conjointly rotating in relation to the fourth part, and the rotational position establishment apparatus is conjointly rotating in relation to the fourth part if the test element is conjointly rotating in relation to the first part.
 6. The method as claimed in claim 4, wherein at least one of the rotational position establishment apparatus and the test element is attached to the rotational device or to the reference rotational device.
 7. The method as claimed in claim 4, wherein the test element is a reflector that reflects radiation incident thereon, and the direction of the reflected radiation is dependent on the relative rotational position between the first part and the fourth part.
 8. The method as claimed in claim 4, wherein: the test element is a measurement body that is arranged at least one of: at a distance from the rotational axis of the rotational device; and in a manner not coaxial with the rotational axis of the rotational device; such that the rotational angle of the measurement body about the rotational axis of the rotational device is determinable by the measuring device on the basis of a changed rotational position of the measurement body.
 9. The method as claimed in claim 1, wherein the reference rotational device is one of a calibrated rotary table, a self-calibrating rotary table and a rotary table that is mechanically adjustable to an accurate rotational position.
 10. The method as claimed in claim 1, wherein the rotational device is one of a rotary table, a rotary joint and a rotary pivot joint.
 11. The method as claimed in claim 1, wherein the rotational axis of the reference rotational device is coaxial or substantially coaxial with the rotational axis of the rotational device.
 12. The method as claimed in claim 1, furthermore comprising the step of: establishing the first resultant rotational position of the first part and of the fourth part relative to one another.
 13. The method as claimed in claim 1, wherein the rotational position error of the rotational position establishment system is established from the changed resultant rotational position of the first part and of the fourth part relative to one another and at least one of: i) the rotational positions of the rotational device or the change in the rotational position of the rotational device; and ii) the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device.
 14. The method as claimed in claim 1, further comprising the steps of: varying the rotational position of the rotational device to a changed rotational position of the rotational device and varying the rotational position of the reference rotational device to a changed rotational position of the reference rotational device such that the resultant rotational position of the first part and of the fourth part has not been changed; establishing the changed rotational position of the rotational device; establishing the changed rotational position of the reference rotational device; and establishing the rotational position error of the rotational position establishment system from the rotational positions of the rotational device or the change in the rotational position of the rotational device, and from the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device.
 15. The method as claimed in claim 1, wherein the reference rotational device includes a rotor and a stator.
 16. An arrangement for establishing one or more errors of a rotational position establishment system that measures rotational positions of parts of a rotational device for a coordinate measuring machine configured to perform the method of claim 1, the arrangement comprising: a rotational device including a first part and a second part rotatable relative to one another about a rotational axis of the rotational device; a rotational position establishment system, a reference rotational device, which includes a rotary table, including a third part and a fourth part rotatable relative to one another about a rotational axis of the reference rotational device, said third part being coupled in a conjointly rotating manner, in relation to the rotational axis of the rotational device, to the second part of the rotational device; a rotational position establishment apparatus for establishing a resultant rotational position of the first part and of the fourth part relative to one another in relation to the rotational axis of the rotational device; an error establishment apparatus for establishing the error of the rotational position establishment system, wherein the error establishment apparatus is configured to establish the rotational position error of the rotational position establishment system from the changed resultant rotational position of the first part and of the fourth part relative to one another.
 17. The arrangement as claimed in claim 16, wherein, the rotational position error of the rotational position establishment system is established from the changed resultant rotational position of the first part and of the fourth part relative to one another and at least one of: i) the rotational positions of the rotational device or the change in the rotational position of the rotational device; and ii) the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device.
 18. The arrangement as claimed in claim 16, wherein the reference rotational device includes a rotor and a stator.
 19. An arrangement for establishing one or more errors of a rotational position establishment system that measures rotational positions of parts of a rotational device for a coordinate measuring machine configured to perform the method of claim 1, the arrangement comprising: a rotational device including a first part and a second part rotatable relative to one another about a rotational axis of the rotational device; a rotational position establishment system, a reference rotational device, which includes a rotary table, including a third part and a fourth part rotatable relative to one another about a rotational axis of the reference rotational device, said third part being coupled in a conjointly rotating manner, in relation to the rotational axis of the rotational device, to the second part of the rotational device; a rotational position establishment apparatus for establishing a resultant rotational position of the first part and of the fourth part relative to one another in relation to the rotational axis of the rotational device; an error establishment apparatus for establishing the error of the rotational position establishment system, wherein the error establishment apparatus is configured to establish the rotational position error of the rotational position establishment system from the rotational positions of the rotational device or the change in the rotational position of the rotational device, and from the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device.
 20. The arrangement as claimed in claim 19, wherein the reference rotational device includes a rotor and a stator.
 21. A method for: establishing one or more errors of a rotational position establishment system that measures rotational positions of parts of a rotational device; and/or establishing a hysteresis effect in the rotational position establishment system, the rotational device including a first part and a second part rotatable relative to one another about a rotational axis of the rotational device, the method comprising the steps of: establishing a first rotational position of the rotational device with first and second parts rotatable relative to one another, wherein a first rotational position of the first part is established relative to the second part of the rotational device; establishing a first rotational position of a reference rotational device, which is a rotary table including a third part and a fourth part rotatable relative to one another, wherein the third part, in relation to the rotational axis, is coupled in a conjointly rotating manner to the second part of the rotational device, and the fourth part is rotatable relative to the third part about a rotational axis of the reference rotational device, wherein a first rotational position of the third part is established relative to the fourth part; wherein a first resultant rotational position of the first part and of the fourth part relative to one another in relation to at least one of the rotational axis of the rotational device and the rotational axis of the reference rotational device results from the first rotational position of the rotational device and the first rotational position of the reference rotational device; varying the rotational position of the rotational device to a second rotational position of the rotational device and varying the rotational position of the reference rotational device to a second rotational position of the reference rotational device such that the resultant rotational position of the first part and of the fourth part has not been changed; wherein the first part is rotated against the second part in one direction, and the third part is rotated against the fourth part in a direction opposite to the one direction when varying the rotational positions of the rotational device and the reference rotational device; establishing the second rotational position of the rotational device; establishing the second rotational position of the reference rotational device; establishing the rotational position error of the rotational position establishment system from the rotational positions of the rotational device or the change in the rotational position of the rotational device, and from the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device; restoring the position of the rotational device to the first rotational position of the rotational device or substantially to the first rotational position of the rotational device and producing a modified first rotational position of the reference rotational device when the first rotational position or substantially the first rotational position of the rotational device is restored; or restoring the position of the reference rotational device to the first rotational position of the reference rotational device or substantially to the first rotational position of the reference rotational device and producing a modified first rotational position of the rotational device when the first rotational position or substantially the first rotational position of the reference rotational device is restored; such that, in the modified first rotational position of the rotational device or the modified first rotational position of the reference rotational device, there is a modified rotational position of the first part and of the fourth part relative to one another, wherein the fourth part is twisted relative to the first part by an angle value compared to the first resultant rotational position of the first part and of the fourth part relative to one another; with the first or substantially the first rotational position of the rotational device and the modified first rotational position of the reference rotational device, or with the first or substantially the first rotational position of the reference rotational device and the modified first rotational position of the rotational device: varying the rotational position of the rotational device to a further rotational position of the rotational device and varying the rotational position of the reference rotational device to a further rotational position of the reference rotational device such that the resultant rotational position of the first part and of the fourth part has not been changed; establishing the further rotational position of the rotational device; establishing the further rotational position of the reference rotational device; establishing the rotational position error of the rotational position establishment system from the rotational positions of the rotational device or the change in the rotational position of the rotational device, and from the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device.
 22. The method as claimed in claim 21, in which the non-changed resultant rotational positions of the first part and of the fourth part relative to one another are established with the aid of a rotational position establishment apparatus.
 23. The method as claimed in claim 22, in which the rotational position establishment apparatus is one or more of an autocollimator, a tactile measuring head system of a coordinate measuring machine, an optical sensor of a coordinate measuring machine, a laser interferometer and a distance sensor.
 24. The method as claimed in claim 22, in which the non-changed resultant rotational position of the first part and of the fourth part relative to one another is established with the aid of a test element, and the rotational position or change in rotational position of the test element relative to the rotational position establishment apparatus is established by means of the rotational position establishment apparatus.
 25. The method as claimed in claim 24, wherein: the rotational position establishment apparatus is positioned in a conjointly rotating manner in relation to one of the first part and the fourth part; the test element is positioned in a conjointly rotating manner in relation to one of the first part and the fourth part; wherein the rotational position establishment apparatus is conjointly rotating in relation to the first part if the test element is conjointly rotating in relation to the fourth part, and the rotational position establishment apparatus is conjointly rotating in relation to the fourth part if the test element is conjointly rotating in relation to the first part.
 26. The method as claimed in claim 24, wherein at least one of the rotational position establishment apparatus and the test element is attached to the rotational device or to the reference rotational device.
 27. The method as claimed in claim 24, wherein the test element is a reflector that reflects radiation incident thereon, and the direction of the reflected radiation is dependent on the relative rotational position between the first part and the fourth part.
 28. The method as claimed in claim 24, wherein: the test element is a measurement body that is arranged at least one of: at a distance from the rotational axis of the rotational device; and in a manner not coaxial with the rotational axis of the rotational device; such that the rotational angle of the measurement body about the rotational axis of the rotational device is determinable by the measuring device on the basis of a changed rotational position of the measurement body.
 29. The method as claimed in claim 21, wherein the reference rotational device is one of a calibrated rotary table, a self-calibrating rotary table and a rotary table that is mechanically adjustable to an accurate rotational position.
 30. The method as claimed in claim 21, wherein the rotational device is one of a rotary table, a rotary joint and a rotary pivot joint.
 31. The method as claimed in claim 21, wherein the rotational axis of the reference rotational device is coaxial or substantially coaxial with the rotational axis of the rotational device.
 32. The method as claimed in claim 21, furthermore comprising the step of: establishing the first resultant rotational position of the first part and of the fourth part relative to one another.
 33. The method as claimed in claim 21, wherein the reference rotational device includes a rotor and a stator.
 34. An arrangement for establishing one or more errors of a rotational position establishment system that measures rotational positions of parts of a rotational device for a coordinate measuring machine configured to perform the method of claim 21, the arrangement comprising: a rotational device including a first part and a second part rotatable relative to one another about a rotational axis of the rotational device; a rotational position establishment system, a reference rotational device, which includes a rotary table, including a third part and a fourth part rotatable relative to one another about a rotational axis of the reference rotational device, said third part being coupled in a conjointly rotating manner, in relation to the rotational axis of the rotational device, to the second part of the rotational device; a rotational position establishment apparatus for establishing a resultant rotational position of the first part and of the fourth part relative to one another in relation to the rotational axis of the rotational device; an error establishment apparatus for establishing the error of the rotational position establishment system, wherein the error establishment apparatus is configured to establish the rotational position error of the rotational position establishment system from the rotational positions of the rotational device or the change in the rotational position of the rotational device, and from the rotational positions of the reference rotational device or the change in the rotational position of the reference rotational device. 